The Modified Block Iterative Algorithms for Asymptotically Relatively Nonexpansive Mappings and the System of Generalized Mixed Equilibrium Problems
The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibri...
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| Vydáno v: | Journal of Applied Mathematics Ročník 2012; číslo 2012; s. 1136 - 1159-281 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cairo, Egypt
Hindawi Limiteds
01.01.2012
Hindawi Publishing Corporation John Wiley & Sons, Inc Wiley |
| Témata: | |
| ISSN: | 1110-757X, 1687-0042 |
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| Abstract | The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many known recent results in the literature. |
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| AbstractList | The propose of this paper is to present a modified block iterative algorithm for
finding a common element between the set of solutions of the fixed points of two
countable families of asymptotically relatively nonexpansive mappings and the
set of solution of the system of generalized mixed equilibrium problems in a
uniformly smooth and uniformly convex Banach space. Our results extend many
known recent results in the literature. The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many known recent results in the literature. |
| Author | Wattanawitoon, Kriengsak Kumam, Poom |
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| CitedBy_id | crossref_primary_10_1155_2012_136134 |
| Cites_doi | 10.1186/1687-1812-2011-9 10.1155/2011/106323 10.1080/02331939608844225 10.1155/2010/869684 10.1016/S0025-5610(96)00071-8 10.1155/2008/284613 10.1007/s10114-011-0099-3 10.1016/j.na.2008.03.058 10.1007/s10957-007-9187-z 10.1155/2010/357120 10.1155/2010/734126 10.1155/2010/123027 10.1007/978-3-642-45780-7_12 10.2307/2313345 10.1016/j.camwa.2011.06.014 10.1155/2009/483497 10.1016/j.nahs.2009.02.006 10.1155/2011/701675 10.1137/S105262340139611X 10.1007/s11590-010-0235-5 10.1155/2008/312454 10.1007/978-94-009-2121-4 10.1016/j.jmaa.2006.08.036 10.1016/j.na.2010.08.021 10.1515/JAA.2001.151 |
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| Copyright | Copyright © 2012 Kriengsak Wattanawitoon and Poom Kumam. Copyright © 2012 Kriengsak Wattanawitoon and Poom Kumam. Kriengsak Wattanawitoon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright 2012 Hindawi Publishing Corporation |
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| References_xml | – volume: 28 start-page: 741 issue: 4 year: 2012 end-page: 758 ident: 15 article-title: Modified block iterative method for solving convex feasibility problem, equilibrium problems and variational inequality problems – volume: 3 start-page: 386 issue: 4 year: 2009 end-page: 394 ident: 25 article-title: Convergence theorems of a hybrid algorithm for equilibrium problems – reference: Cioranescu I. 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A weak convergence theorem for the alternating method with Bregman distances Theory and Applications of Nonlinear Operators of Accretive and Monotone Type 1996 178 New York, NY, USA Dekker 313 318 Lecture Notes in Pure and Applied Mathematics 1386686 ZBL0943.47040 – volume: 331 start-page: 506 issue: 1 year: 2007 end-page: 515 ident: 4 article-title: Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces – volume: 70 start-page: 2707 issue: 7 year: 2009 end-page: 2716 ident: 20 article-title: Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings – volume: 2011 year: 2011 end-page: 16 ident: 27 article-title: A new hybrid algorithm for solving a system of generalized mixed equilibrium problems, solving a family of quasi- -asymptotically nonexpansive mappings, and obtaining common fixed points in Banach space – volume: 2011 year: 2011 ident: e_1_2_5_8_2 article-title: The shrinking projection method for solving generalized equilibrium problems and common fixed points for asymptotically quasi-φ-nonexpansive mappings publication-title: Fixed Point Theory and Applications doi: 10.1186/1687-1812-2011-9 – start-page: 313 volume-title: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type year: 1996 ident: e_1_2_5_17_2 – ident: e_1_2_5_27_2 doi: 10.1155/2011/106323 – ident: e_1_2_5_22_2 doi: 10.1080/02331939608844225 – ident: e_1_2_5_26_2 doi: 10.1155/2010/869684 – ident: e_1_2_5_2_2 doi: 10.1016/S0025-5610(96)00071-8 – volume: 2008 year: 2008 ident: e_1_2_5_19_2 article-title: Strong convergence of monotone hybrid algorithm for hemi-relatively nonexpansive mappings publication-title: Fixed Point Theory and Applications doi: 10.1155/2008/284613 – volume-title: Nonlinear Functional Analysis year: 2000 ident: e_1_2_5_29_2 – ident: e_1_2_5_15_2 doi: 10.1007/s10114-011-0099-3 – ident: e_1_2_5_20_2 doi: 10.1016/j.na.2008.03.058 – ident: e_1_2_5_13_2 doi: 10.1007/s10957-007-9187-z – ident: e_1_2_5_6_2 doi: 10.1155/2010/357120 – ident: e_1_2_5_11_2 doi: 10.1155/2010/734126 – ident: e_1_2_5_7_2 doi: 10.1155/2010/123027 – ident: e_1_2_5_3_2 doi: 10.1007/978-3-642-45780-7_12 – ident: e_1_2_5_16_2 doi: 10.2307/2313345 – ident: e_1_2_5_10_2 doi: 10.1016/j.camwa.2011.06.014 – volume: 2009 year: 2009 ident: e_1_2_5_24_2 article-title: Strong convergence theorems of modified Ishikawa iterations for countable hemi-relatively nonexpansive mappings in a Banach space publication-title: Fixed Point Theory and Applications doi: 10.1155/2009/483497 – ident: e_1_2_5_25_2 doi: 10.1016/j.nahs.2009.02.006 – ident: e_1_2_5_9_2 doi: 10.1155/2011/701675 – ident: e_1_2_5_31_2 doi: 10.1137/S105262340139611X – volume: 63 start-page: 123 year: 1994 ident: e_1_2_5_1_2 article-title: From optimization and variational inequalities to equilibrium problems publication-title: The Mathematics Student – ident: e_1_2_5_14_2 doi: 10.1007/s11590-010-0235-5 – volume: 6 start-page: 117 year: 2005 ident: e_1_2_5_5_2 article-title: Equilibrium programming in Hilbert spaces publication-title: Journal of Nonlinear and Convex Analysis – start-page: 609 volume-title: Nonlinear Analysis and Convex Analysis year: 2006 ident: e_1_2_5_12_2 – volume: 2008 year: 2008 ident: e_1_2_5_18_2 article-title: Strong convergence to common fixed points of countable relatively quasi-nonexpansive mappings publication-title: Fixed Point Theory and Applications doi: 10.1155/2008/312454 – ident: e_1_2_5_28_2 doi: 10.1007/978-94-009-2121-4 – ident: e_1_2_5_4_2 doi: 10.1016/j.jmaa.2006.08.036 – start-page: 15 volume-title: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type year: 1996 ident: e_1_2_5_30_2 – ident: e_1_2_5_23_2 doi: 10.1016/j.na.2010.08.021 – ident: e_1_2_5_21_2 doi: 10.1515/JAA.2001.151 |
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| Snippet | The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of... The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of... |
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| SubjectTerms | Algorithms Asymptotic properties Banach space Blocking Economic models Iterative algorithms Mapping Mathematical analysis Studies |
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| Title | The Modified Block Iterative Algorithms for Asymptotically Relatively Nonexpansive Mappings and the System of Generalized Mixed Equilibrium Problems |
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| Volume | 2012 |
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