Fixed point and best proximity point theorems for contractions in new class of probabilistic metric spaces

Fixexd point theory and applications

Yongfu Su¹  Jingling Zhang¹ 

[1] Department of Mathematics, Tianjin Polytechnic University, Tianjin, P.R. China

关键词: probabilistic metric spaces;    contraction;    fixed point;    best proximity point;    mathematical expectation;   

DOI  :  10.1186/1687-1812-2014-170

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to present some definitions and basic concepts of best proximity point in a new class of probabilistic metric spaces and to prove the best proximity point theorems for the contractive mappings and weak contractive mappings. In order to get the best proximity point theorems, some new probabilistic contraction mapping principles have been proved. Meanwhile the error estimate inequalities have been established. Further, a method of the proof is also new and interesting, which is to use the mathematical expectation of the distribution function studying the related problems.

【 授权许可】

CC BY