Fixed point theorems for cyclic self-maps involving weaker Meir-Keeler functions in complete metric spaces and applications

Fixexd point theory and applications

Hemant Kumar Nashine¹  Salvador Romaguera² 

[1] Department of Mathematics, Disha Institute of Management and Technology, Raipur, India;Instituto Universitario de Matemácnica de València, Valencia, Spain;tica Pura y Aplicada, Universitat Politè

关键词: fixed point;    cyclic map;    weaker Meir-Keeler function;    complete metric space;    integral equation;   

DOI  :  10.1186/1687-1812-2013-224

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We obtain fixed point theorems for cyclic self-maps on complete metric spaces involving Meir-Keeler and weaker Meir-Keeler functions, respectively. In this way, we extend several well-known fixed point theorems and, in particular, improve some very recent results on weaker Meir-Keeler functions. Fixed point results for well-posed property and for limit shadowing property are also deduced. Finally, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented. MSC:47H10, 54H25, 54E50, 45G10.

【 授权许可】

CC BY