Best proximity point theorems: unriddling a special nonlinear programming problem
This paper addresses the non-linear programming problem of globally minimizing the real valued function x ⟶ d ( x , Sx ) where S is a generalized proximal contraction in the setting of a metric space. Eventually, one can obtain optimal approximate solutions to some fixed-point equations in the event...
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| Published in: | TOP Vol. 22; no. 2; pp. 543 - 553 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2014
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| ISSN: | 1134-5764, 1863-8279 |
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| Abstract | This paper addresses the non-linear programming problem of globally minimizing the real valued function
x
⟶
d
(
x
,
Sx
) where
S
is a generalized proximal contraction in the setting of a metric space. Eventually, one can obtain optimal approximate solutions to some fixed-point equations in the event that they have no solution. |
|---|---|
| AbstractList | This paper addresses the non-linear programming problem of globally minimizing the real valued function
x
⟶
d
(
x
,
Sx
) where
S
is a generalized proximal contraction in the setting of a metric space. Eventually, one can obtain optimal approximate solutions to some fixed-point equations in the event that they have no solution. |
| Author | Sadiq Basha, S. |
| Author_xml | – sequence: 1 givenname: S. surname: Sadiq Basha fullname: Sadiq Basha, S. email: drssb@yahoo.com organization: Department of Mathematics, Anna University |
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| Cites_doi | 10.1016/j.na.2008.04.037 10.1016/j.na.2007.08.064 10.1007/s10898-009-9521-0 10.1016/j.na.2007.10.014 10.1016/j.na.2010.06.008 10.1081/NFA-120026380 10.1016/j.jat.2011.06.012 10.1016/j.na.2008.07.022 10.1155/2009/197308 10.1007/s10957-011-9869-4 10.1016/j.na.2011.04.017 10.1016/j.na.2009.07.024 10.1080/01630563.2010.485713 10.1007/s10957-010-9745-7 10.1016/j.jmaa.2005.10.081 10.1006/jath.1999.3415 10.1155/2010/946178 10.1016/j.aml.2010.12.043 |
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| Issue | 2 |
| Keywords | Generalized proximal contraction Non-linear programming problem Global optimization 90C30 Generalized proximal cyclic contraction Optimal approximate solution Proximal contraction Proximal cyclic contraction 90C26 Best proximity point Fixed point |
| Language | English |
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| References | Vetro (CR19) 2010; 73 Sankar Raj (CR17) 2011; 74 Shahzad, Sadiq Basha, Jeyaraj (CR18) 2011; 148 Di Bari, Suzuki, Vetro (CR3) 2008; 69 Derafshpour, Rezapour, Shahzad (CR2) 2011; 37 Rezapour, Derafshpour, Shahzad (CR8) 2010; 2010 Sadiq Basha, Shahzad, Jeyaraj (CR16) 2011; 24 Sadiq Basha, Veeramani (CR15) 2000; 103 Al-Thagafi, Shahzad (CR1) 2009; 70 Wlodarczyk, Plebaniak, Obczyński (CR22) 2010; 72 Karpagam, Agrawal (CR5) 2009; 2009 Wlodarczyk, Plebaniak, Banach (CR20) 2009; 70 Sadiq Basha (CR14) 2011; 151 Kirk, Reich, Veeramani (CR7) 2003; 24 Sadiq Basha (CR12) 2011 Sadiq Basha (CR9) 2010; 31 Sadiq Basha (CR10) 2011; 49 Wlodarczyk, Plebaniak, Banach (CR21) 2009; 71 Kikkawa, Suzuki (CR6) 2008; 69 Eldred, Veeramani (CR4) 2006; 323 Sadiq Basha (CR11) 2011; 163 Sadiq Basha (CR13) 2011; 74 S Sadiq Basha (269_CR15) 2000; 103 K Wlodarczyk (269_CR21) 2009; 71 K Wlodarczyk (269_CR20) 2009; 70 Sh Rezapour (269_CR8) 2010; 2010 S Sadiq Basha (269_CR10) 2011; 49 M Kikkawa (269_CR6) 2008; 69 C Vetro (269_CR19) 2010; 73 C Di Bari (269_CR3) 2008; 69 S Sadiq Basha (269_CR9) 2010; 31 M Derafshpour (269_CR2) 2011; 37 WA Kirk (269_CR7) 2003; 24 S Sadiq Basha (269_CR12) 2011 AA Eldred (269_CR4) 2006; 323 V Sankar Raj (269_CR17) 2011; 74 S Sadiq Basha (269_CR13) 2011; 74 S Sadiq Basha (269_CR14) 2011; 151 MA Al-Thagafi (269_CR1) 2009; 70 S Karpagam (269_CR5) 2009; 2009 S Sadiq Basha (269_CR16) 2011; 24 N Shahzad (269_CR18) 2011; 148 S Sadiq Basha (269_CR11) 2011; 163 K Wlodarczyk (269_CR22) 2010; 72 |
| References_xml | – volume: 74 start-page: 4804 year: 2011 end-page: 4808 ident: CR17 article-title: A best proximity point theorem for weakly contractive non-self-mappings publication-title: Fuel Energy Abstr – volume: 70 start-page: 3332 year: 2009 end-page: 3341 ident: CR20 article-title: Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces publication-title: Nonlinear Anal doi: 10.1016/j.na.2008.04.037 – volume: 69 start-page: 2942 year: 2008 end-page: 2949 ident: CR6 article-title: Three fixed point theorems for generalized contractions with constants in complete metric spaces publication-title: Nonlinear Anal doi: 10.1016/j.na.2007.08.064 – volume: 49 start-page: 15 year: 2011 end-page: 21 ident: CR10 article-title: Best proximity points: global optimal approximate solutions publication-title: J Glob Optim doi: 10.1007/s10898-009-9521-0 – volume: 69 start-page: 3790 year: 2008 end-page: 3794 ident: CR3 article-title: Best proximity points for cyclic Meir-Keeler contractions publication-title: Nonlinear Anal doi: 10.1016/j.na.2007.10.014 – volume: 73 start-page: 2283 year: 2010 end-page: 2291 ident: CR19 article-title: Best proximity points: convergence and existence theorems for p-cyclic mappings publication-title: Nonlinear Anal doi: 10.1016/j.na.2010.06.008 – volume: 24 start-page: 851 year: 2003 end-page: 862 ident: CR7 article-title: Proximinal retracts and best proximity pair theorems publication-title: Numer Funct Anal Optim doi: 10.1081/NFA-120026380 – volume: 163 start-page: 1772 year: 2011 end-page: 1781 ident: CR11 article-title: Best proximity point theorems publication-title: J Approx Theory doi: 10.1016/j.jat.2011.06.012 – volume: 70 start-page: 3665 year: 2009 end-page: 3671 ident: CR1 article-title: Convergence and existence results for best proximity points publication-title: Nonlinear Anal doi: 10.1016/j.na.2008.07.022 – year: 2011 ident: CR12 article-title: Common best proximity points: global minimal solutions publication-title: Top – volume: 2009 year: 2009 ident: CR5 article-title: Best proximity point theorems for p-cyclic Meir-Keeler contractions publication-title: Fixed Point Theory Appl doi: 10.1155/2009/197308 – volume: 151 start-page: 210 year: 2011 end-page: 216 ident: CR14 article-title: Best proximity points: optimal solutions publication-title: J Optim Theory Appl doi: 10.1007/s10957-011-9869-4 – volume: 74 start-page: 5844 year: 2011 end-page: 5850 ident: CR13 article-title: Best proximity point theorems generalizing the contraction principle publication-title: Nonlinear Anal doi: 10.1016/j.na.2011.04.017 – volume: 72 start-page: 794 year: 2010 end-page: 805 ident: CR22 article-title: Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces publication-title: Nonlinear Anal doi: 10.1016/j.na.2009.07.024 – volume: 31 start-page: 1 year: 2010 end-page: 8 ident: CR9 article-title: Extensions of Banach’s contraction principle publication-title: Numer Funct Anal Optim doi: 10.1080/01630563.2010.485713 – volume: 148 start-page: 69 year: 2011 end-page: 78 ident: CR18 article-title: Common best proximity points: global optimal solutions publication-title: J Optim Theory Appl doi: 10.1007/s10957-010-9745-7 – volume: 323 start-page: 1001 year: 2006 end-page: 1006 ident: CR4 article-title: Existence and convergence of best proximity points publication-title: J Math Anal Appl doi: 10.1016/j.jmaa.2005.10.081 – volume: 103 start-page: 119 year: 2000 end-page: 129 ident: CR15 article-title: Best proximity pair theorems for multifunctions with open fibres publication-title: J Approx Theory doi: 10.1006/jath.1999.3415 – volume: 71 start-page: 3583 year: 2009 end-page: 3586 ident: CR21 article-title: Erratum to: “Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces” publication-title: Nonlinear Anal – volume: 37 start-page: 193 year: 2011 end-page: 202 ident: CR2 article-title: Best proximity points of cyclic -contractions on reflexive Banach space publication-title: Topol Methods Nonlinear Anal – volume: 2010 year: 2010 ident: CR8 article-title: Best proximity points of cyclic -contractions in ordered metric spaces publication-title: Fixed Point Theory Appl doi: 10.1155/2010/946178 – volume: 24 start-page: 883 year: 2011 end-page: 886 ident: CR16 article-title: Common best proximity points: global optimization of multi-objective functions publication-title: Appl Math Lett doi: 10.1016/j.aml.2010.12.043 – volume: 49 start-page: 15 year: 2011 ident: 269_CR10 publication-title: J Glob Optim doi: 10.1007/s10898-009-9521-0 – volume: 24 start-page: 883 year: 2011 ident: 269_CR16 publication-title: Appl Math Lett doi: 10.1016/j.aml.2010.12.043 – volume: 24 start-page: 851 year: 2003 ident: 269_CR7 publication-title: Numer Funct Anal Optim doi: 10.1081/NFA-120026380 – volume: 70 start-page: 3332 year: 2009 ident: 269_CR20 publication-title: Nonlinear Anal doi: 10.1016/j.na.2008.04.037 – volume: 103 start-page: 119 year: 2000 ident: 269_CR15 publication-title: J Approx Theory doi: 10.1006/jath.1999.3415 – volume: 72 start-page: 794 year: 2010 ident: 269_CR22 publication-title: Nonlinear Anal doi: 10.1016/j.na.2009.07.024 – volume: 69 start-page: 3790 year: 2008 ident: 269_CR3 publication-title: Nonlinear Anal doi: 10.1016/j.na.2007.10.014 – volume: 37 start-page: 193 year: 2011 ident: 269_CR2 publication-title: Topol Methods Nonlinear Anal – volume: 151 start-page: 210 year: 2011 ident: 269_CR14 publication-title: J Optim Theory Appl doi: 10.1007/s10957-011-9869-4 – volume: 163 start-page: 1772 year: 2011 ident: 269_CR11 publication-title: J Approx Theory doi: 10.1016/j.jat.2011.06.012 – volume: 31 start-page: 1 year: 2010 ident: 269_CR9 publication-title: Numer Funct Anal Optim doi: 10.1080/01630563.2010.485713 – volume: 73 start-page: 2283 year: 2010 ident: 269_CR19 publication-title: Nonlinear Anal doi: 10.1016/j.na.2010.06.008 – volume: 71 start-page: 3583 year: 2009 ident: 269_CR21 publication-title: Nonlinear Anal – volume: 74 start-page: 4804 year: 2011 ident: 269_CR17 publication-title: Fuel Energy Abstr – volume: 2010 year: 2010 ident: 269_CR8 publication-title: Fixed Point Theory Appl doi: 10.1155/2010/946178 – volume: 70 start-page: 3665 year: 2009 ident: 269_CR1 publication-title: Nonlinear Anal doi: 10.1016/j.na.2008.07.022 – volume: 74 start-page: 5844 year: 2011 ident: 269_CR13 publication-title: Nonlinear Anal doi: 10.1016/j.na.2011.04.017 – year: 2011 ident: 269_CR12 publication-title: Top – volume: 323 start-page: 1001 year: 2006 ident: 269_CR4 publication-title: J Math Anal Appl doi: 10.1016/j.jmaa.2005.10.081 – volume: 148 start-page: 69 year: 2011 ident: 269_CR18 publication-title: J Optim Theory Appl doi: 10.1007/s10957-010-9745-7 – volume: 2009 year: 2009 ident: 269_CR5 publication-title: Fixed Point Theory Appl doi: 10.1155/2009/197308 – volume: 69 start-page: 2942 year: 2008 ident: 269_CR6 publication-title: Nonlinear Anal doi: 10.1016/j.na.2007.08.064 |
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x
⟶
d
(
x
,
Sx
) where
S
is a generalized proximal... |
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| SubjectTerms | Business and Management Economic Theory/Quantitative Economics/Mathematical Methods Economics Finance Industrial and Production Engineering Insurance Management Operations Research/Decision Theory Optimization Original Paper Statistics for Business |
| Title | Best proximity point theorems: unriddling a special nonlinear programming problem |
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