Best proximity results: optimization by approximate solutions

Fixexd point theory and applications

Georgeta Maniu¹  Binayak S Choudhury²  Pulak Konar³  Nikhilesh Metiya⁴ 

[1] Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploiesti, Ploiesti, Romania;Department of Mathematics, Indian Institute of Engineering Science and Technology, Howrah, India;Department of Mathematics, NITMAS, Alipore, India;Department of Mathematics, Sovarani Memorial College, Howrah, India

关键词: partially ordered metric space;    best proximity point;    fixed point equation;    approximate solution;    optimization;    47H10;    54H10;    54H25;   

DOI  :  10.1186/s13663-016-0569-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we utilize a generalized weakly contractive mapping to establish some best proximity point results which are global optimization results for finding the minimum distances between two sets. Amongst many approaches to this problem, we adopt the approach where the problem is treated as that of finding global optimal approximate solution of the fixed point equation for the generalized weak contraction mapping. We use three control functions to define such mappings. The results are obtained in metric spaces with a partial ordering defined therein. There is a blending of analytic and order theoretic approaches in the proofs. The uniqueness is obtained by imposing some order theoretic conditions additionally. There are several corollaries. An illustration of the main theorem through an example is given which also shows that the corollaries are properly contained in the main theorem.

【 授权许可】

CC BY