Some fixed point theorems in Menger PbM-spaces with an application

Fixexd point theory and applications

Mahnaz Khanehgir¹  Firoozeh Hasanvand¹ 

[1] Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

关键词: contractive mapping;    fixed point;    b-metric space;    Menger probabilistic metric space;    Volterra integral equation;    47H10;    37C25;    54H25;    55M20;   

DOI  :  10.1186/s13663-015-0326-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we establish the structure of Menger PbM-spaces as a generalization of Menger PM-spaces. We present some fixed point theorems for a new class of contractive mappings in the framework of Menger PbM-spaces. We also provide examples to illustrate the results presented herein. Then we utilize our main result to obtain the existence and uniqueness of a solution for a Volterra type integral equation.

【 授权许可】

CC BY