Reich–Krasnoselskii-type fixed point results with applications in integral equations

Journal of Inequalities and Applications

Research

Faryad Ali¹  Nayyar Mehmood²  Niaz Ahmad²  Akbar Azam³ 

[1] Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), PO Box 90950, 11623, Riyadh, Saudi Arabia;Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan;Department of Mathematics, Grand Asian University Sialkot, 7KM, Pasrur Road 51310, Sialkot, Pakistan;

关键词: Generalized Kannan contraction;    Generalized Reich contraction;    Krasnoselskii;    Fixed point;    Integral equations;    47H10;    54H25;   

DOI  :  10.1186/s13660-023-03022-z

 received in 2022-09-10, accepted in 2023-08-16,  发布年份 2023

来源: Springer

【 摘 要 】

In this paper, motivated by Reich contraction and tool of measure of noncompactness, some generalizations of Reich, Kannan, Darbo, Sadovskii, and Krasnoselskii type fixed point results are presented by considering a pair of maps A, B on a nonempty closed subset M of a Banach space X into X. The existence of a solution to the equation Ax+Bx=x\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$Ax+Bx=x$\end{document}, where A is k-set contractive and B is a generalized Reich contraction, is established. As applications, it is established that the main result of this paper can be applied to learn conditions under which a solution of a nonlinear integral equation exists. Further we explain this phenomenon with the help of a practical example to approximate such solutions by using fixed point techniques. The graphs of exact and approximate solutions are also given to attract readers for further research activities.

【 授权许可】

CC BY   
© Springer Nature Switzerland AG 2023

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