Inertial Krasnosel’skiǐ–Mann type hybrid algorithms for solving hierarchical fixed point problems
In this paper, we suggest two inertial Krasnosel’skiǐ–Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space. We prove strong convergence theorems for these algorithms and the conditions of the convergence are very weak...
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| Published in: | Fixed point theory and algorithms for sciences and engineering Vol. 21; no. 2; pp. 1 - 22 |
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01.06.2019
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| ISSN: | 1661-7738, 1661-7746, 2730-5422 |
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| Abstract | In this paper, we suggest two inertial Krasnosel’skiǐ–Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space. We prove strong convergence theorems for these algorithms and the conditions of the convergence are very weak comparing other algorithms for the hierarchical fixed point problems. Further, we derive some consequences from the main results. Finally, we present two academic numerical examples for comparing these two algorithms with the algorithm in Dong et al. (J Fixed Point Theory A 19(4):3097–3118,
2017
), which illustrate the advantage of the proposed algorithms. The methods and results presented in this paper generalize and unify previously known corresponding methods and results of this area. |
|---|---|
| AbstractList | In this paper, we suggest two inertial Krasnosel’skiǐ–Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space. We prove strong convergence theorems for these algorithms and the conditions of the convergence are very weak comparing other algorithms for the hierarchical fixed point problems. Further, we derive some consequences from the main results. Finally, we present two academic numerical examples for comparing these two algorithms with the algorithm in Dong et al. (J Fixed Point Theory A 19(4):3097–3118, 2017), which illustrate the advantage of the proposed algorithms. The methods and results presented in this paper generalize and unify previously known corresponding methods and results of this area. In this paper, we suggest two inertial Krasnosel’skiǐ–Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space. We prove strong convergence theorems for these algorithms and the conditions of the convergence are very weak comparing other algorithms for the hierarchical fixed point problems. Further, we derive some consequences from the main results. Finally, we present two academic numerical examples for comparing these two algorithms with the algorithm in Dong et al. (J Fixed Point Theory A 19(4):3097–3118, 2017 ), which illustrate the advantage of the proposed algorithms. The methods and results presented in this paper generalize and unify previously known corresponding methods and results of this area. |
| ArticleNumber | 57 |
| Author | Kazmi, K. R. Ali, Rehan Dong, Qiao-Li Li, Xiao-Huan |
| Author_xml | – sequence: 1 givenname: Qiao-Li orcidid: 0000-0001-6765-4437 surname: Dong fullname: Dong, Qiao-Li email: dongql@lsec.cc.ac.cn organization: College of Science, Civil Aviation University of China – sequence: 2 givenname: K. R. surname: Kazmi fullname: Kazmi, K. R. organization: Department of Mathematics, Faculty of Science and Arts-Rabigh, King Abdulaziz University, Department of Mathematics, Aligarh Muslim University – sequence: 3 givenname: Rehan surname: Ali fullname: Ali, Rehan organization: Department of Mathematics, Jamia Millia Islamia – sequence: 4 givenname: Xiao-Huan surname: Li fullname: Li, Xiao-Huan organization: College of Science, Civil Aviation University of China |
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| CitedBy_id | crossref_primary_10_1155_2021_9421449 crossref_primary_10_1007_s41478_023_00695_z crossref_primary_10_1155_2023_6177912 crossref_primary_10_1186_s13660_020_02313_z crossref_primary_10_1016_j_cam_2022_115010 crossref_primary_10_1186_s13660_021_02749_x crossref_primary_10_1155_2021_3653807 crossref_primary_10_1002_mma_9467 crossref_primary_10_1016_j_cnsns_2024_108076 crossref_primary_10_3390_axioms10030147 crossref_primary_10_1080_02331934_2022_2043857 crossref_primary_10_1186_s13660_021_02565_3 crossref_primary_10_1186_s13662_021_03384_y crossref_primary_10_1007_s00500_023_08921_3 crossref_primary_10_1186_s13660_021_02591_1 crossref_primary_10_1007_s13398_021_01049_9 crossref_primary_10_3390_math10101751 |
| Cites_doi | 10.1088/0266-5611/24/1/015015 10.1023/A:1011253113155 10.1007/s10898-017-0506-0 10.1007/s11075-017-0316-y 10.1137/15100463X 10.1016/j.cam.2007.07.021 10.1088/0266-5611/23/4/015 10.1137/S0363012998335802 10.1137/120866877 10.1137/130910294 10.1016/j.jmaa.2008.03.028 10.1007/s11075-015-0007-5 10.1080/02331934.2018.1522636 10.1007/BF01581204 10.1016/S0377-0427(02)00906-8 10.1007/s10898-014-0150-x 10.1007/s11784-017-0472-7 10.1137/050624315 10.1137/110849456 10.1016/j.na.2004.11.011 10.1088/0266-5611/20/1/006 10.1016/S0022-247X(02)00458-4 10.1137/080716542 10.1007/s11590-016-1102-9 10.1016/j.na.2005.08.018 10.1007/s11784-017-0435-z 10.1088/0266-5611/27/4/045009 10.1016/0022-247X(79)90024-6 10.1137/0314056 10.1088/0266-5611/22/3/006 10.1137/S105262340343467X 10.1017/CBO9780511983658 10.1081/NFA-200045815 10.1007/s10851-014-0523-2 10.1007/s11075-017-0448-0 |
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| References | Malitsky, Semenov (CR31) 2015; 61 Brézis (CR7) 1973 Yamada, Ogura (CR44) 2004; 25 Bot, Csetnek, Hendrich (CR5) 2015; 256 Chen, Huang, Zhang (CR11) 2013; 29 He, Yang, Duan (CR19) 2010; 217 Chan, Ma, Yang (CR10) 2015; 8 Shehu, Iyiola (CR43) 2017; 19 Alvarez (CR1) 2000; 38 Micchelli, Shen, Xu (CR33) 2011; 27 Byrne (CR8) 2004; 20 Kazmi, Rizvi, Ali (CR24) 2015; 24 Dong, Jiang, Cholamjiak, Shehu (CR13) 2017; 19 Korpelevich (CR26) 1976; 12 Iiduka (CR20) 2012; 22 Iiduka (CR21) 2013; 23 Popov (CR39) 1980; 28 Reich (CR40) 1979; 67 Kazmi, Ali, Furkan (CR22) 2018; 77 Dong, Lu (CR14) 2015; 2015 Maingé (CR29) 2008; 219 Dong, Cho, Zhong, Rassias (CR12) 2018; 70 Rockafellar (CR41) 1976; 14 Moudafi, Oliny (CR34) 2003; 155 Yao, Liou (CR46) 2008; 24 Moudafi (CR36) 2007; 23 Yang, Zhao (CR45) 2006; 22 Maingé (CR30) 2008; 344 Bot, Csetnek (CR6) 2016; 71 Cabot (CR9) 2005; 15 Eckstein, Bertsekas (CR16) 1992; 55 Goebel, Kirk (CR17) 1990 Nakajo, Takahashi (CR38) 2003; 279 Dong, Yuan, Cho, Rassias (CR15) 2018; 12 Luo, Pang, Ralph (CR28) 1996 Nadezhkina, Takahashi (CR37) 2006; 16 Matinez-Yanes, Xu (CR32) 2006; 64 Alvarez, Attouch (CR2) 2001; 9 Kim, Xu (CR25) 2005; 61 Shehu, Dong, Jiang (CR42) 2019; 68 Beck, Teboulle (CR4) 2009; 2 Moudafi, Maige (CR35) 2006; 2006 Kazmi, Ali, Furkan (CR23) 2018; 79 Lorenz, Pock (CR27) 2015; 51 Goebel, Reich (CR18) 1984 Attouch, Peypouquet, Redont (CR3) 2014; 24 A Beck (699_CR4) 2009; 2 Q Dong (699_CR13) 2017; 19 P Chen (699_CR11) 2013; 29 A Cabot (699_CR9) 2005; 15 TH Kim (699_CR25) 2005; 61 LD Popov (699_CR39) 1980; 28 YV Malitsky (699_CR31) 2015; 61 F Alvarez (699_CR2) 2001; 9 A Moudafi (699_CR35) 2006; 2006 N Nadezhkina (699_CR37) 2006; 16 QL Dong (699_CR14) 2015; 2015 K Goebel (699_CR18) 1984 H Iiduka (699_CR20) 2012; 22 RT Rockafellar (699_CR41) 1976; 14 S He (699_CR19) 2010; 217 H Iiduka (699_CR21) 2013; 23 QL Dong (699_CR15) 2018; 12 Q Yang (699_CR45) 2006; 22 J Eckstein (699_CR16) 1992; 55 D Lorenz (699_CR27) 2015; 51 Y Shehu (699_CR43) 2017; 19 PE Maingé (699_CR30) 2008; 344 PE Maingé (699_CR29) 2008; 219 RH Chan (699_CR10) 2015; 8 KR Kazmi (699_CR23) 2018; 79 A Moudafi (699_CR36) 2007; 23 Y Yao (699_CR46) 2008; 24 ZQ Luo (699_CR28) 1996 GM Korpelevich (699_CR26) 1976; 12 KR Kazmi (699_CR22) 2018; 77 KR Kazmi (699_CR24) 2015; 24 S Reich (699_CR40) 1979; 67 H Attouch (699_CR3) 2014; 24 QL Dong (699_CR12) 2018; 70 A Moudafi (699_CR34) 2003; 155 I Yamada (699_CR44) 2004; 25 F Alvarez (699_CR1) 2000; 38 CA Micchelli (699_CR33) 2011; 27 K Nakajo (699_CR38) 2003; 279 H Brézis (699_CR7) 1973 C Matinez-Yanes (699_CR32) 2006; 64 RI Bot (699_CR6) 2016; 71 Y Shehu (699_CR42) 2019; 68 K Goebel (699_CR17) 1990 RI Bot (699_CR5) 2015; 256 C Byrne (699_CR8) 2004; 20 |
| References_xml | – volume: 24 start-page: 501 year: 2008 end-page: 508 ident: CR46 article-title: Weak and strong convergence of Krasnoselski–Mann iteration for hierarchical fixed-point problems publication-title: Inverse Probl. doi: 10.1088/0266-5611/24/1/015015 – volume: 29 start-page: 025011, 33 year: 2013 ident: CR11 article-title: A primal–dual fixed point algorithm for convex separable minimization with applications to image restoration publication-title: Inverse Probl. – volume: 9 start-page: 3 year: 2001 end-page: 11 ident: CR2 article-title: An inertial proximalmethod for maximal monotone operators via discretization of a nonlinear oscillator with damping publication-title: Set-Valued Anal. doi: 10.1023/A:1011253113155 – volume: 70 start-page: 687 year: 2018 end-page: 704 ident: CR12 article-title: Inertial projection and contraction algorithms for variational inequalities publication-title: J. Global Optim. doi: 10.1007/s10898-017-0506-0 – volume: 77 start-page: 289 year: 2018 end-page: 308 ident: CR22 article-title: Krasnoselski–Mann type iterative method for hierarchical fixed point problem and split mixed equilibrium problem publication-title: Numer. Algorithms doi: 10.1007/s11075-017-0316-y – volume: 12 start-page: 747 year: 1976 end-page: 756 ident: CR26 article-title: The extragradient method for finding saddle points and other problems publication-title: Matecon – volume: 8 start-page: 2239 issue: 4 year: 2015 end-page: 2267 ident: CR10 article-title: Inertial proximal ADMM for linearly constrained separable convex optimization publication-title: SIAM J. Imaging Sci. doi: 10.1137/15100463X – volume: 219 start-page: 223 year: 2008 end-page: 236 ident: CR29 article-title: Convergence theorem for inertial KM-type algorithms publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.07.021 – volume: 23 start-page: 1635 year: 2007 end-page: 1640 ident: CR36 article-title: Krasnoselski–Mann iteration for hierarchical fixed-point problems publication-title: Inverse Probl. doi: 10.1088/0266-5611/23/4/015 – volume: 38 start-page: 1102 issue: 4 year: 2000 end-page: 1119 ident: CR1 article-title: On the minimizing property of a second order dissipative system in Hilbert spaces publication-title: SIAM J. Control Optim. doi: 10.1137/S0363012998335802 – volume: 23 start-page: 1 year: 2013 end-page: 26 ident: CR21 article-title: Fixed point optimization algorithms for distributed optimization in networkd systems publication-title: SIAM. J. Optim. doi: 10.1137/120866877 – volume: 24 start-page: 232 issue: 4 year: 2014 end-page: 256 ident: CR3 article-title: A dynamical approach to an inertial forward–backward algorithm for convex minimization publication-title: SIAM J. Optim. doi: 10.1137/130910294 – volume: 344 start-page: 876 year: 2008 end-page: 887 ident: CR30 article-title: Regularized and inertial algorithms for common fixed points of nonlinear operators publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2008.03.028 – volume: 28 start-page: 777 issue: 5 year: 1980 end-page: 784 ident: CR39 article-title: A modification of the Arrow–Hurwicz method for searching for saddle points publication-title: Mat. Zametki – volume: 71 start-page: 519 year: 2016 end-page: 540 ident: CR6 article-title: An inertial forward–backward–forward primal–dual splitting algorithm for solving monotone inclusion problems publication-title: Numer. Algorithm doi: 10.1007/s11075-015-0007-5 – volume: 68 start-page: 385 year: 2019 end-page: 409 ident: CR42 article-title: Single projection method for pseudo-monotone variational inequality in Hilbert spaces publication-title: Optimization doi: 10.1080/02331934.2018.1522636 – volume: 2015 start-page: 7 issue: 37 year: 2015 ident: CR14 article-title: A new hybrid algorithm for a nonexpansive mapping publication-title: Fixed Point Theory Appl. – volume: 55 start-page: 293 year: 1992 end-page: 318 ident: CR16 article-title: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators publication-title: Math. Program. doi: 10.1007/BF01581204 – volume: 155 start-page: 447 year: 2003 end-page: 454 ident: CR34 article-title: Convergence of a splitting inertial proximal method for monotone operators publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(02)00906-8 – volume: 61 start-page: 193 year: 2015 end-page: 202 ident: CR31 article-title: A hybrid method without extrapolating step for solving variational inequality problems publication-title: J. Global Optim. doi: 10.1007/s10898-014-0150-x – volume: 19 start-page: 3097 issue: 4 year: 2017 end-page: 3118 ident: CR13 article-title: A strong convergence result involving an inertial forward–backward algorithm for monotone inclusions publication-title: J. Fixed Point Theory A doi: 10.1007/s11784-017-0472-7 – volume: 16 start-page: 1230 year: 2006 end-page: 1241 ident: CR37 article-title: Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings publication-title: SIAM J. Optim. doi: 10.1137/050624315 – volume: 22 start-page: 862 year: 2012 end-page: 878 ident: CR20 article-title: Iterative algorithm for triple-hierarchical constrained noncnvex optimization problem and its application to network bandwith allocation publication-title: SIAM. J. Optim. doi: 10.1137/110849456 – volume: 61 start-page: 51 year: 2005 end-page: 60 ident: CR25 article-title: Strong convergence of modified Mann iterations publication-title: Nonlinear Anal. doi: 10.1016/j.na.2004.11.011 – volume: 20 start-page: 103 year: 2004 end-page: 120 ident: CR8 article-title: A unified treatment of some iterative algorithms in signal processing and image reconstruction publication-title: Inverse Probl. doi: 10.1088/0266-5611/20/1/006 – volume: 279 start-page: 372 year: 2003 end-page: 379 ident: CR38 article-title: Strong convergence theorems for nonexpansive mappings and nonexpansive semigroup publication-title: J. Math. Anal. Appl. doi: 10.1016/S0022-247X(02)00458-4 – volume: 2 start-page: 183 issue: 1 year: 2009 end-page: 202 ident: CR4 article-title: A fast iterative shrinkage-thersholding algorithm for linear inverse problems publication-title: SIAM J. Imaging Sci. doi: 10.1137/080716542 – volume: 256 start-page: 472 year: 2015 end-page: 487 ident: CR5 article-title: Inertial Douglas–Rachford splitting for monotone inclusion problems publication-title: Appl. Math. Comput. – volume: 12 start-page: 87 issue: 1 year: 2018 end-page: 102 ident: CR15 article-title: Modified inertial Mann algorithm and inertial CQ-algorithm for nonexpansive mappings publication-title: Optim. Lett. doi: 10.1007/s11590-016-1102-9 – volume: 64 start-page: 2400 year: 2006 end-page: 2411 ident: CR32 article-title: Strong convergence of the CQ method for fixed point processes publication-title: Nonlinear Anal. doi: 10.1016/j.na.2005.08.018 – year: 1973 ident: CR7 publication-title: Mathematical Studies 5 – volume: 217 start-page: 4239 year: 2010 end-page: 4247 ident: CR19 article-title: Realization of the hybrid method for Mann iterations publication-title: Appl. Math. Comput. – volume: 19 start-page: 2483 year: 2017 end-page: 2510 ident: CR43 article-title: Convergence analysis for the proximal split feasibility problem using an inertial extrapolation term method publication-title: J. Fixed Point Theory Appl. doi: 10.1007/s11784-017-0435-z – volume: 2006 start-page: 10 issue: 95453 year: 2006 ident: CR35 article-title: Towards viscosity approximations of hierarchical fixed-point problems publication-title: Fixed Point Theory Appl. – volume: 27 start-page: 045009 issue: 4 year: 2011 ident: CR33 article-title: Proximity algorithms for image models: denoising publication-title: Inverse Probl. doi: 10.1088/0266-5611/27/4/045009 – volume: 67 start-page: 274 year: 1979 end-page: 276 ident: CR40 article-title: Weak convergence theorems for nonexpansive mappings in Banach spaces publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(79)90024-6 – volume: 14 start-page: 877 issue: 5 year: 1976 end-page: 898 ident: CR41 article-title: Monotone operators and the proximal point algorithm publication-title: SIAM J. Control Optim. doi: 10.1137/0314056 – volume: 24 start-page: 163 issue: 2 year: 2015 end-page: 170 ident: CR24 article-title: A hybrid iterative method without extrapolating step for solving mixed equilibrium problem publication-title: Creative Math. Inf. – year: 1990 ident: CR17 publication-title: Cambridge Studies in Advanced Mathematics – volume: 22 start-page: 833 year: 2006 end-page: 844 ident: CR45 article-title: Generalized KM theorem and their applications publication-title: Inverse Probl. doi: 10.1088/0266-5611/22/3/006 – volume: 15 start-page: 555 year: 2005 end-page: 572 ident: CR9 article-title: Proximal point algorithm controlled by a slowly vanishing term: application to hierarchical minimization publication-title: SIAM J. Optim. doi: 10.1137/S105262340343467X – year: 1996 ident: CR28 publication-title: Mathematical Programs with Equilibrium Constraints doi: 10.1017/CBO9780511983658 – volume: 25 start-page: 619 year: 2004 end-page: 655 ident: CR44 article-title: Hybrid steepest descent method for the variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings publication-title: Numer. Funct. Anal. Optim. doi: 10.1081/NFA-200045815 – volume: 51 start-page: 311 year: 2015 end-page: 325 ident: CR27 article-title: An inertial forward–backward algorithm for monotone inclusions publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-014-0523-2 – volume: 79 start-page: 499 year: 2018 end-page: 527 ident: CR23 article-title: Hybrid iterative method for split monotone variational inclusion problem and hierarchical fixed point problem for a finite family of nonexpansive mappings publication-title: Numer. Algorithms doi: 10.1007/s11075-017-0448-0 – year: 1984 ident: CR18 publication-title: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings – volume: 256 start-page: 472 year: 2015 ident: 699_CR5 publication-title: Appl. Math. Comput. – volume: 77 start-page: 289 year: 2018 ident: 699_CR22 publication-title: Numer. Algorithms doi: 10.1007/s11075-017-0316-y – volume: 12 start-page: 87 issue: 1 year: 2018 ident: 699_CR15 publication-title: Optim. Lett. doi: 10.1007/s11590-016-1102-9 – volume: 217 start-page: 4239 year: 2010 ident: 699_CR19 publication-title: Appl. Math. Comput. – volume: 51 start-page: 311 year: 2015 ident: 699_CR27 publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-014-0523-2 – volume: 19 start-page: 2483 year: 2017 ident: 699_CR43 publication-title: J. Fixed Point Theory Appl. doi: 10.1007/s11784-017-0435-z – volume: 27 start-page: 045009 issue: 4 year: 2011 ident: 699_CR33 publication-title: Inverse Probl. doi: 10.1088/0266-5611/27/4/045009 – volume: 344 start-page: 876 year: 2008 ident: 699_CR30 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2008.03.028 – volume: 19 start-page: 3097 issue: 4 year: 2017 ident: 699_CR13 publication-title: J. Fixed Point Theory A doi: 10.1007/s11784-017-0472-7 – volume-title: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings year: 1984 ident: 699_CR18 – volume: 28 start-page: 777 issue: 5 year: 1980 ident: 699_CR39 publication-title: Mat. Zametki – volume: 8 start-page: 2239 issue: 4 year: 2015 ident: 699_CR10 publication-title: SIAM J. Imaging Sci. doi: 10.1137/15100463X – volume: 24 start-page: 232 issue: 4 year: 2014 ident: 699_CR3 publication-title: SIAM J. Optim. doi: 10.1137/130910294 – volume: 2015 start-page: 7 issue: 37 year: 2015 ident: 699_CR14 publication-title: Fixed Point Theory Appl. – volume: 61 start-page: 193 year: 2015 ident: 699_CR31 publication-title: J. Global Optim. doi: 10.1007/s10898-014-0150-x – volume: 79 start-page: 499 year: 2018 ident: 699_CR23 publication-title: Numer. Algorithms doi: 10.1007/s11075-017-0448-0 – volume: 155 start-page: 447 year: 2003 ident: 699_CR34 publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(02)00906-8 – volume: 70 start-page: 687 year: 2018 ident: 699_CR12 publication-title: J. Global Optim. doi: 10.1007/s10898-017-0506-0 – volume: 38 start-page: 1102 issue: 4 year: 2000 ident: 699_CR1 publication-title: SIAM J. Control Optim. doi: 10.1137/S0363012998335802 – volume: 23 start-page: 1635 year: 2007 ident: 699_CR36 publication-title: Inverse Probl. doi: 10.1088/0266-5611/23/4/015 – volume: 2 start-page: 183 issue: 1 year: 2009 ident: 699_CR4 publication-title: SIAM J. Imaging Sci. doi: 10.1137/080716542 – volume-title: Mathematical Studies 5 year: 1973 ident: 699_CR7 – volume: 61 start-page: 51 year: 2005 ident: 699_CR25 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2004.11.011 – volume: 23 start-page: 1 year: 2013 ident: 699_CR21 publication-title: SIAM. J. Optim. doi: 10.1137/120866877 – volume: 24 start-page: 163 issue: 2 year: 2015 ident: 699_CR24 publication-title: Creative Math. Inf. – volume: 67 start-page: 274 year: 1979 ident: 699_CR40 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(79)90024-6 – volume: 24 start-page: 501 year: 2008 ident: 699_CR46 publication-title: Inverse Probl. doi: 10.1088/0266-5611/24/1/015015 – volume: 71 start-page: 519 year: 2016 ident: 699_CR6 publication-title: Numer. Algorithm doi: 10.1007/s11075-015-0007-5 – volume: 20 start-page: 103 year: 2004 ident: 699_CR8 publication-title: Inverse Probl. doi: 10.1088/0266-5611/20/1/006 – volume-title: Cambridge Studies in Advanced Mathematics year: 1990 ident: 699_CR17 – volume: 219 start-page: 223 year: 2008 ident: 699_CR29 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.07.021 – volume: 55 start-page: 293 year: 1992 ident: 699_CR16 publication-title: Math. Program. doi: 10.1007/BF01581204 – volume: 16 start-page: 1230 year: 2006 ident: 699_CR37 publication-title: SIAM J. Optim. doi: 10.1137/050624315 – volume: 64 start-page: 2400 year: 2006 ident: 699_CR32 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2005.08.018 – volume: 15 start-page: 555 year: 2005 ident: 699_CR9 publication-title: SIAM J. Optim. doi: 10.1137/S105262340343467X – volume: 2006 start-page: 10 issue: 95453 year: 2006 ident: 699_CR35 publication-title: Fixed Point Theory Appl. – volume: 25 start-page: 619 year: 2004 ident: 699_CR44 publication-title: Numer. Funct. Anal. Optim. doi: 10.1081/NFA-200045815 – volume: 68 start-page: 385 year: 2019 ident: 699_CR42 publication-title: Optimization doi: 10.1080/02331934.2018.1522636 – volume: 279 start-page: 372 year: 2003 ident: 699_CR38 publication-title: J. Math. Anal. Appl. doi: 10.1016/S0022-247X(02)00458-4 – volume: 29 start-page: 025011, 33 year: 2013 ident: 699_CR11 publication-title: Inverse Probl. – volume: 12 start-page: 747 year: 1976 ident: 699_CR26 publication-title: Matecon – volume: 22 start-page: 833 year: 2006 ident: 699_CR45 publication-title: Inverse Probl. doi: 10.1088/0266-5611/22/3/006 – volume: 9 start-page: 3 year: 2001 ident: 699_CR2 publication-title: Set-Valued Anal. doi: 10.1023/A:1011253113155 – volume: 22 start-page: 862 year: 2012 ident: 699_CR20 publication-title: SIAM. J. Optim. doi: 10.1137/110849456 – volume-title: Mathematical Programs with Equilibrium Constraints year: 1996 ident: 699_CR28 doi: 10.1017/CBO9780511983658 – volume: 14 start-page: 877 issue: 5 year: 1976 ident: 699_CR41 publication-title: SIAM J. Control Optim. doi: 10.1137/0314056 |
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| SubjectTerms | Algorithms Analysis Convergence Fixed points (mathematics) Hilbert space Iterative methods Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics |
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| Title | Inertial Krasnosel’skiǐ–Mann type hybrid algorithms for solving hierarchical fixed point problems |
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