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Reich–Krasnoselskii-type fixed point results with applications in integral equations.
- Source :
-
Journal of Inequalities & Applications . 10/16/2023, Vol. 2023 Issue 1, p1-17. 17p. - Publication Year :
- 2023
-
Abstract
- 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 A x + B x = x , 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2023
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 173017328
- Full Text :
- https://doi.org/10.1186/s13660-023-03022-z