Best proximity point theorems for generalized proximal contractions

Fixexd point theory and applications

S Sadiq Basha¹  N Shahzad² 

[1] Department of Mathematics, Anna University, Chennai, India;Department of Mathematics, King Abdul Aziz University, Jeddah, Saudi Arabia

关键词: optimal approximate solution;    fixed point;    best proximity point;    contraction;    generalized proximal contraction;   

DOI  :  10.1186/1687-1812-2012-42

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Best proximity point theorems unravel the techniques for determining an optimal approximate solution, designated as a best proximity point, to the equation Tx = x which is likely to have no solution when T is a non-self mapping. This article presents best proximity point theorems for new classes of non-self mappings, known as generalized proximal contractions, in the setting of metric spaces. Further, the famous Banach's contraction principle and some of its generalizations and variants are realizable as special cases of the aforesaid best proximity point theorems. Mathematics Subject Classification: 41A65; 46B20; 47H10.

【 授权许可】

CC BY