Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation

Demonstratio mathematica

article

Habib ur Rehman¹  Dhananjay Gopal²  Poom Kumam¹ 

[1] Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT);National Institute of Technology

关键词: Darbo fixed point theorem;    measure of noncompactness;    fixed point;    coupled fixed point;    functional integral equation;   

DOI  :  10.1515/dema-2019-0012

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

In this paper, we provide some generalizations of the Darbo’s fixed point theorem associated with the measure of noncompactness and present some results on the existence of the coupled fixed point theorems for a special class of operators in a Banach space. To acquire this result, we define α - ψ and β - ψ condensing operators and using them we propose new fixed point results. Our results generalize and extend some comparable results from the literature. Additionally, as an application, we apply the obtained fixed point theorems to study the nonlinear functional integral equations.

【 授权许可】

CC BY