Generalized contraction mapping principle and generalized best proximity point theorems in probabilistic metric spaces

Fixexd point theory and applications

Jen-Chih Yao¹  Yongfu Su²  Wenbiao Gao² 

[1] Center for General Education, China Medical University, Taichung, Taiwan;Department of Mathematics, Tianjin Polytechnic University, Tianjin, P.R. China

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

DOI  :  10.1186/s13663-015-0323-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to introduce some basic definitions about fixed point and best proximity point in two classes of probabilistic metric spaces and to prove contraction mapping principle and relevant best proximity point theorems. The first class is the so-called S-probabilistic metric spaces. In S-probabilistic metric spaces, the generalized contraction mapping principle and generalized best proximity point theorems have been proved by authors. These results improve and extend the recent results of Su and Zhang (Fixed Point Theory Appl. 2014:170, 2014). The second class is the so-called Menger probabilistic metric spaces. In Menger probabilistic metric spaces, the contraction mapping principle and relevant best proximity point theorems have been proved by authors. These results also improve and extend the results of many authors. In order to get the results of this paper, some new methods have been used. Meanwhile some error estimate inequalities have been established.

【 授权许可】

CC BY