A new bound for the Jensen gap pertaining twice differentiable functions with applications
In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the main result in information theory.
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| Veröffentlicht in: | Advances in difference equations Jg. 2020; H. 1; S. 1 - 11 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Springer International Publishing
06.07.2020
Springer Nature B.V SpringerOpen |
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| ISSN: | 1687-1847, 1687-1839, 1687-1847 |
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| Abstract | In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the main result in information theory. |
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| AbstractList | In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the main result in information theory. Abstract In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the main result in information theory. |
| ArticleNumber | 333 |
| Author | Khan, Shahid Adil Khan, Muhammad Chu, Yu-Ming Butt, Saad Ihsan |
| Author_xml | – sequence: 1 givenname: Shahid surname: Khan fullname: Khan, Shahid organization: Department of Mathematics, University of Peshawar – sequence: 2 givenname: Muhammad surname: Adil Khan fullname: Adil Khan, Muhammad organization: Department of Mathematics, University of Peshawar – sequence: 3 givenname: Saad Ihsan surname: Butt fullname: Butt, Saad Ihsan organization: Department of Mathematics, Comsats Institute of Information Technology – sequence: 4 givenname: Yu-Ming surname: Chu fullname: Chu, Yu-Ming email: chuyuming2005@126.com organization: Department of Mathematics, Huzhou University, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology |
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| Cites_doi | 10.1007/978-94-015-8034-2 10.1007/s40840-017-0526-4 10.1002/mma.6066 10.3390/e20080608 10.5666/KMJ.2012.52.4.495 10.1016/j.physleta.2020.126460 10.1002/mma.5858 10.3390/math7100956 10.3934/math.2020027 10.1186/s13660-019-2112-9 10.1186/s13660-018-1923-4 10.1016/j.laa.2012.12.011 10.1007/s13398-020-00843-1 10.1186/s13660-018-1625-y 10.1016/j.automatica.2015.08.025 10.3934/math.2020074 10.1002/mma.4531 10.1016/0895-7177(96)00085-4 10.1016/j.spl.2019.03.006 10.3390/math7100896 10.1007/s10473-019-0520-z 10.3934/math.2020315 10.1186/s13660-018-1902-9 10.1016/j.mcm.2010.05.035 10.11650/twjm/1500405733 10.1080/00031305.2017.1419145 10.1007/978-3-319-05311-0 |
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| References | Bainov, Simeonov (CR9) 1992 Kim (CR22) 2016; 64 Adil Khan, Khalid, Pečarić (CR4) 2012; 52 Gujrati (CR16) 2020 Dragomir, Goh (CR15) 1996; 24 Liao, Berg (CR23) 2019; 73 Song, Adil Khan, Zaheer Ullah, Chu (CR32) 2018; 2018 Pečarić, Pečarić, Rodić (CR29) 2018; 2018 Adil Khan, Pečarić, Chu (CR7) 2020; 5 Rashid, Noor, Noor, Safdar, Chu (CR31) 2019; 7 Lovričević, Pečarić, Pečarić (CR25) 2018; 2018 Wang, Zhang, Chu (CR33) 2019; 39B Adil Khan, Hanif, Hameed Khan, Ahmad, Chu (CR3) 2019; 2019 Adil Khan, Al-sahwi, Chu (CR1) 2018; 20 Dragomir (CR13) 2010; 52 Agarwal, Yadav, Baleanu, Purohit (CR8) 2020; 5 Mishra, Baleanu, Tchier, Purohit (CR26) 2019; 7 Niaz, Khan, Pečarić (CR28) 2020; 4 Adil Khan, Pečarić, Pečarić (CR5) 2017; 40 Cloud, Drachman, Lebedev (CR11) 2014 Khan, Adil Khan, Chu (CR19) 2020; 43 Adil Khan, Pečarić, Pečarić (CR6) 2019; 42 Dragomir (CR14) 2010; 14 Khan, Niaz, Pečarić, Pečarić (CR18) 2018; 2018 Dragomir (CR12) 2004; 29 Horváth, Pečarić, Pečarić (CR17) 2019; 42 Adil Khan, Ali Khan, Ali, Kilicman (CR2) 2015; 262 Lin (CR24) 2019; 151 Budimir, Dragomir, Pečarić (CR10) 2001; 2 Kian (CR21) 2014; 456 Khan, Adil Khan, Chu (CR20) 2020; 114 Purohit, Jolly, Bansal, Singh, Kumar (CR30) 2020; 6 Mishra, Kumar, Purohit (CR27) 2020; 5 M. Kian (2794_CR21) 2014; 456 S.S. Dragomir (2794_CR12) 2004; 29 S.S. Dragomir (2794_CR14) 2010; 14 T. Niaz (2794_CR28) 2020; 4 S. Rashid (2794_CR31) 2019; 7 M. Adil Khan (2794_CR1) 2018; 20 M.J. Cloud (2794_CR11) 2014 M. Adil Khan (2794_CR2) 2015; 262 K.A. Khan (2794_CR18) 2018; 2018 M. Adil Khan (2794_CR7) 2020; 5 M. Adil Khan (2794_CR5) 2017; 40 S.S. Dragomir (2794_CR15) 1996; 24 R. Agarwal (2794_CR8) 2020; 5 S.S. Dragomir (2794_CR13) 2010; 52 J.G. Liao (2794_CR23) 2019; 73 M. Adil Khan (2794_CR6) 2019; 42 A.M. Mishra (2794_CR26) 2019; 7 L. Horváth (2794_CR17) 2019; 42 Y.-Q. Song (2794_CR32) 2018; 2018 P.D. Gujrati (2794_CR16) 2020 S. Khan (2794_CR20) 2020; 114 M.-K. Wang (2794_CR33) 2019; 39B A.M. Mishra (2794_CR27) 2020; 5 D. Bainov (2794_CR9) 1992 S.D. Purohit (2794_CR30) 2020; 6 M. Adil Khan (2794_CR3) 2019; 2019 J.-H. Kim (2794_CR22) 2016; 64 M. Adil Khan (2794_CR4) 2012; 52 N. Lovričević (2794_CR25) 2018; 2018 Q. Lin (2794_CR24) 2019; 151 I. Budimir (2794_CR10) 2001; 2 Ð. Pečarić (2794_CR29) 2018; 2018 S. Khan (2794_CR19) 2020; 43 |
| References_xml | – volume: 2 issue: 1 year: 2001 ident: CR10 article-title: Further reverse results for Jensen’s discrete inequality and applications in information theory publication-title: J. Inequal. Pure Appl. Math. – year: 2014 ident: CR11 publication-title: Inequalities with Applications to Engineering – year: 1992 ident: CR9 publication-title: Integral Inequalities and Applications doi: 10.1007/978-94-015-8034-2 – volume: 42 start-page: 933 issue: 3 year: 2019 end-page: 946 ident: CR17 article-title: Estimations of - and Rényi divergences by using a cyclic refinement of the Jensen’s inequality publication-title: Bull. Malays. Math. Sci. Soc. doi: 10.1007/s40840-017-0526-4 – volume: 43 start-page: 2577 year: 2020 end-page: 2587 ident: CR19 article-title: Converses of the Jensen inequality derived from the Green functions with applications in information theory publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.6066 – volume: 20 issue: 8 year: 2018 ident: CR1 article-title: New estimations for Shannon and Zipf–Mandelbrot entropies publication-title: Entropy doi: 10.3390/e20080608 – volume: 52 start-page: 495 year: 2012 end-page: 511 ident: CR4 article-title: Improvement of Jensen’s inequality in terms of Gâteaux derivatives for convex functions in linear spaces with applications publication-title: Kyungpook Math. J. doi: 10.5666/KMJ.2012.52.4.495 – year: 2020 ident: CR16 article-title: Jensen inequality and the second law publication-title: Phys. Lett. A doi: 10.1016/j.physleta.2020.126460 – volume: 42 start-page: 7411 issue: 18 year: 2019 end-page: 7424 ident: CR6 article-title: Bounds for Csiszár divergence and hybrid Zipf–Mandelbrot entropy publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.5858 – volume: 7 year: 2019 ident: CR31 article-title: Hermite–Hadamard type inequalities for the class of convex functions on time scale publication-title: Mathematics doi: 10.3390/math7100956 – volume: 5 start-page: 399 issue: 1 year: 2020 end-page: 407 ident: CR27 article-title: Unified integral inequalities comprising pathway operators publication-title: AIMS Math. doi: 10.3934/math.2020027 – volume: 2019 year: 2019 ident: CR3 article-title: Association of Jensen’s inequality for -convex function with Csiszár divergence publication-title: J. Inequal. Appl. doi: 10.1186/s13660-019-2112-9 – volume: 2018 year: 2018 ident: CR29 article-title: About the sharpness of the Jensen inequality publication-title: J. Inequal. Appl. doi: 10.1186/s13660-018-1923-4 – volume: 456 start-page: 82 year: 2014 end-page: 87 ident: CR21 article-title: Operator Jensen inequality for superquadratic functions publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2012.12.011 – volume: 114 year: 2020 ident: CR20 article-title: New converses of Jensen inequality via Green functions with applications publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. doi: 10.1007/s13398-020-00843-1 – volume: 2018 year: 2018 ident: CR25 article-title: Zipf–Mandelbrot law, -divergences and the Jensen-type interpolating inequalities publication-title: J. Inequal. Appl. doi: 10.1186/s13660-018-1625-y – volume: 64 start-page: 121 year: 2016 end-page: 125 ident: CR22 article-title: Further improvement of Jensen inequality and application to stability of time-delayed systems publication-title: Automatica doi: 10.1016/j.automatica.2015.08.025 – volume: 5 start-page: 1062 issue: 2 year: 2020 end-page: 1073 ident: CR8 article-title: Existence and uniqueness of miscible flow equation through porous media with a nonsingular fractional derivative publication-title: AIMS Math. doi: 10.3934/math.2020074 – volume: 40 start-page: 7316 issue: 18 year: 2017 end-page: 7322 ident: CR5 article-title: Bounds for Shannon and Zipf–Mandelbrot entropies publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.4531 – volume: 24 start-page: 1 issue: 2 year: 1996 end-page: 11 ident: CR15 article-title: A counterpart of Jensen’s discrete inequality for differentiable convex mappings and applications in information theory publication-title: Math. Comput. Model. doi: 10.1016/0895-7177(96)00085-4 – volume: 151 start-page: 79 year: 2019 end-page: 83 ident: CR24 article-title: Jensen inequality for superlinear expectations publication-title: Stat. Probab. Lett. doi: 10.1016/j.spl.2019.03.006 – volume: 7 issue: 10 year: 2019 ident: CR26 article-title: Certain results comprising the weighted Chebyshev functional using pathway fractional integrals publication-title: Mathematics doi: 10.3390/math7100896 – volume: 262 start-page: 128 year: 2015 end-page: 135 ident: CR2 article-title: On the refinement of Jensen’s inequality publication-title: Appl. Math. Comput. – volume: 4 start-page: 70 issue: 1 year: 2020 end-page: 80 ident: CR28 article-title: On refinement of Jensen’s inequality for 3-convex function at a point publication-title: Turk. J. Ineq. – volume: 39B start-page: 1440 issue: 5 year: 2019 end-page: 1450 ident: CR33 article-title: Monotonicity, convexity and inequalities involving the generalized elliptic integrals publication-title: Acta Math. Sci. doi: 10.1007/s10473-019-0520-z – volume: 5 start-page: 4931 issue: 5 year: 2020 end-page: 4945 ident: CR7 article-title: Refinements of Jensen’s and McShane’s inequalities with applications publication-title: AIMS Math. doi: 10.3934/math.2020315 – volume: 2018 year: 2018 ident: CR18 article-title: Refinement of Jensen’s inequality and estimation of f-and Rényi divergence via Montgomery identity publication-title: J. Inequal. Appl. doi: 10.1186/s13660-018-1902-9 – volume: 29 start-page: 77 issue: 1 year: 2004 end-page: 88 ident: CR12 article-title: A converse of the Jensen inequality for convex mappings of several variables and applications publication-title: Acta Math. Vietnam. – volume: 6 start-page: 29 year: 2020 end-page: 38 ident: CR30 article-title: Chebyshev type inequalities involving the fractional integral operator containing multi-index Mittag-Leffler function in the kernel publication-title: Appl. Appl. Math. Spec. Issue – volume: 52 start-page: 1497 year: 2010 end-page: 1505 ident: CR13 article-title: A new refinement of Jensen’s inequality in linear spaces with applications publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2010.05.035 – volume: 14 start-page: 153 issue: 1 year: 2010 end-page: 164 ident: CR14 article-title: A refinement of Jensen’s inequality with applications for -divergence measures publication-title: Taiwan. J. Math. doi: 10.11650/twjm/1500405733 – volume: 2018 year: 2018 ident: CR32 article-title: Integral inequalities involving strongly convex functions publication-title: J. Funct. Spaces – volume: 73 start-page: 278 issue: 3 year: 2019 end-page: 281 ident: CR23 article-title: Sharpening Jensen’s inequality publication-title: Am. Stat. doi: 10.1080/00031305.2017.1419145 – volume: 20 issue: 8 year: 2018 ident: 2794_CR1 publication-title: Entropy doi: 10.3390/e20080608 – volume: 2019 year: 2019 ident: 2794_CR3 publication-title: J. Inequal. Appl. doi: 10.1186/s13660-019-2112-9 – volume: 7 issue: 10 year: 2019 ident: 2794_CR26 publication-title: Mathematics doi: 10.3390/math7100896 – volume: 456 start-page: 82 year: 2014 ident: 2794_CR21 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2012.12.011 – volume: 24 start-page: 1 issue: 2 year: 1996 ident: 2794_CR15 publication-title: Math. Comput. Model. doi: 10.1016/0895-7177(96)00085-4 – volume: 73 start-page: 278 issue: 3 year: 2019 ident: 2794_CR23 publication-title: Am. Stat. doi: 10.1080/00031305.2017.1419145 – volume: 4 start-page: 70 issue: 1 year: 2020 ident: 2794_CR28 publication-title: Turk. J. Ineq. – volume: 2018 year: 2018 ident: 2794_CR32 publication-title: J. Funct. Spaces – volume: 64 start-page: 121 year: 2016 ident: 2794_CR22 publication-title: Automatica doi: 10.1016/j.automatica.2015.08.025 – volume: 52 start-page: 1497 year: 2010 ident: 2794_CR13 publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2010.05.035 – year: 2020 ident: 2794_CR16 publication-title: Phys. Lett. A doi: 10.1016/j.physleta.2020.126460 – volume: 2018 year: 2018 ident: 2794_CR29 publication-title: J. Inequal. Appl. doi: 10.1186/s13660-018-1923-4 – volume: 151 start-page: 79 year: 2019 ident: 2794_CR24 publication-title: Stat. Probab. Lett. doi: 10.1016/j.spl.2019.03.006 – volume: 42 start-page: 7411 issue: 18 year: 2019 ident: 2794_CR6 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.5858 – volume: 5 start-page: 4931 issue: 5 year: 2020 ident: 2794_CR7 publication-title: AIMS Math. doi: 10.3934/math.2020315 – volume-title: Inequalities with Applications to Engineering year: 2014 ident: 2794_CR11 doi: 10.1007/978-3-319-05311-0 – volume: 29 start-page: 77 issue: 1 year: 2004 ident: 2794_CR12 publication-title: Acta Math. Vietnam. – volume: 42 start-page: 933 issue: 3 year: 2019 ident: 2794_CR17 publication-title: Bull. Malays. Math. Sci. Soc. doi: 10.1007/s40840-017-0526-4 – volume: 114 year: 2020 ident: 2794_CR20 publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. doi: 10.1007/s13398-020-00843-1 – volume: 14 start-page: 153 issue: 1 year: 2010 ident: 2794_CR14 publication-title: Taiwan. J. Math. doi: 10.11650/twjm/1500405733 – volume: 262 start-page: 128 year: 2015 ident: 2794_CR2 publication-title: Appl. Math. Comput. – volume: 2 issue: 1 year: 2001 ident: 2794_CR10 publication-title: J. Inequal. Pure Appl. Math. – volume: 2018 year: 2018 ident: 2794_CR25 publication-title: J. Inequal. Appl. doi: 10.1186/s13660-018-1625-y – volume: 6 start-page: 29 year: 2020 ident: 2794_CR30 publication-title: Appl. Appl. Math. Spec. Issue – volume: 43 start-page: 2577 year: 2020 ident: 2794_CR19 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.6066 – volume: 7 year: 2019 ident: 2794_CR31 publication-title: Mathematics doi: 10.3390/math7100956 – volume: 52 start-page: 495 year: 2012 ident: 2794_CR4 publication-title: Kyungpook Math. J. doi: 10.5666/KMJ.2012.52.4.495 – volume: 2018 year: 2018 ident: 2794_CR18 publication-title: J. Inequal. Appl. doi: 10.1186/s13660-018-1902-9 – volume: 40 start-page: 7316 issue: 18 year: 2017 ident: 2794_CR5 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.4531 – volume: 39B start-page: 1440 issue: 5 year: 2019 ident: 2794_CR33 publication-title: Acta Math. Sci. doi: 10.1007/s10473-019-0520-z – volume: 5 start-page: 1062 issue: 2 year: 2020 ident: 2794_CR8 publication-title: AIMS Math. doi: 10.3934/math.2020074 – volume-title: Integral Inequalities and Applications year: 1992 ident: 2794_CR9 doi: 10.1007/978-94-015-8034-2 – volume: 5 start-page: 399 issue: 1 year: 2020 ident: 2794_CR27 publication-title: AIMS Math. doi: 10.3934/math.2020027 |
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| Snippet | In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as... Abstract In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder... |
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| SubjectTerms | Analysis Applications Convex function Csiszár divergence Difference and Functional Equations Functional Analysis Green function Green's functions Hölder inequality Information theory Jensen inequality Mathematics Mathematics and Statistics Methods Ordinary Differential Equations Partial Differential Equations Topics in Special Functions and q-Special Functions: Theory |
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| Title | A new bound for the Jensen gap pertaining twice differentiable functions with applications |
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