Global optimization using $\alpha$-ordered proximal contractions in metric spaces with partial orders

Somayya Komal; Poom Kumam

doi:10.4995/agt.2016.5180

Authors

Somayya Komal King Mongkut's University of Technology Thonburi
Poom Kumam King Mongkut's University of Technology Thonburi https://orcid.org/0000-0002-5463-4581

DOI:

https://doi.org/10.4995/agt.2016.5180

Keywords:

common best proximity point, global optimal approximate solution, proximally increasing mappings, $\alpha$-ordered contractions, $\alpha$-ordered proximal contraction, $\alpha$-ordered proximal cyclic contraction

Abstract

The purpose of this article is to establish the global optimization with partial orders for the pair of non-self mappings, by introducing new type of contractions like $\alpha$-ordered contractions and $\alpha$-ordered proximal contraction in the frame work of complete metric spaces. Also calculates some fixed point theorems with the help of these generalized contractions. In addition, established an example to show the validity of our main result. These results extended and unify many existing results in the literature.

Downloads

Download data is not yet available.

Author Biographies

Somayya Komal, King Mongkut's University of Technology Thonburi

Department of Mathematics, Faculty of Science

Poom Kumam, King Mongkut's University of Technology Thonburi

Department of Mathematics, Faculty of Science ;Theoretical and Computational Science (TaCS) Center, Science Laboratory Building

References

A. Akbar and M. Gabeleh, Global optimal solutions of noncyclic mappings in metric spaces, J. Optim. Theory Appl. 153 (2012), 298-305. https://doi.org/10.1007/s10957-011-9966-4

A. M. Al-Thagafi and N. Shahzad, Best proximity pairs and equilibriam pairs for Kakutani multimaps, Nonlinear Anal. 70 (2009), 1209-1216. https://doi.org/10.1016/j.na.2008.02.004

A. M. Al-Thagafi and N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Anal. 70 (2009), 3665-3671. https://doi.org/10.1016/j.na.2008.07.022

S. S. Basha, Extensions of Banach's contraction principle, Numer. Funct. Anal. Optim. 31 (2010), 569-576. https://doi.org/10.1080/01630563.2010.485713

S. S. Basha, Best proximity points: Global optimal approximate solution, J. Glob. Optim. 49 (2010), 15-21. https://doi.org/10.1007/s10898-009-9521-0

S. S. Basha, Best proximity point theorems generalizing the contraction principle, Nonlinear Anal. 74 (2011) 5844-5850. https://doi.org/10.1016/j.na.2011.04.017

S. S. Basha, Common best proximity points: Global minimization of multi-objective functions, J. Glob. Optim. 54 (2012), 367-373. https://doi.org/10.1007/s10898-011-9760-8

S. S. Basha, Common best proximity points: Global minimal solutions, TOP 21 (2011), 182-188. https://doi.org/10.1007/s11750-011-0171-2

S. S. Basha, Global optimization in metric spaces with partial orders, Optimization 63 (2014), 817-825. https://doi.org/10.1080/02331934.2012.685238

S. S. Basha, N. Shahzad and R. Jeyaraj, Best proximity points: Approximation and optimization, Optim. Lett. 7 (2011), 145-155. https://doi.org/10.1007/s11590-011-0404-1

S. S. Basha, N. Shahzad and R. Jeyaraj, Optimal approximate solutions of fixed point equations, Abstract Appl. Anal. 2011 (2011), Article ID 174560, 9 pages. https://doi.org/10.1155/2011/174560

S. S. Basha, N. Shahzad and R. Jeyaraj, Common best proximity points: Global optimization of multi-objective functions, Appl. Math. Lett. 24 (2011), 883-886. https://doi.org/10.1016/j.aml.2010.12.043

S. S. Basha and P. Veeramani, Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory 103 (2000), 119-129. https://doi.org/10.1006/jath.1999.3415

A. A. Eldered and P. Veeramani, Proximinal normal structure and relatively nonexpansive mappings, Studia Math. 171 (2005), 283-293. https://doi.org/10.4064/sm171-3-5

J. M. Felicit and A. A. Eldred, Best proximity points for cyclical contractive mappings, Applied Gen. Topol. 16 (2015), 119-126. https://doi.org/10.4995/agt.2015.3242

C. Vetro, Best proximity points: Convergence and existence theorems for $p$-cyclic mappings, Nonlinear Anal. 73 (2010), 2283-2291. https://doi.org/10.1016/j.na.2010.06.008