International Journal of Nonlinear Analysis and Applications

Some $\psi-$fixed point theorems of Wardowski kind in $\mathcal{G}$-metric spaces with application to integral equations

Document Type : Research Paper

Author

Department of Mathematics, K.R.M.D.A.V. College, Nakodar-144040, Punjab, India

Abstract

In this manuscript, we introduce new notions of generalized ($\mathfrak{f^{*}}, \psi)$-contraction and utilize this concept to prove some fixed point results for lower semi-continuous $\psi$-mapping satisfying certain conditions in the frame of G-metric spaces. Our results improve the results of [6] and [8] by omitting the continuity condition of $F\in \Im$ with the aid of the $\psi$-fixed point. We give an illustrative example to help accessibility of the got results and to show the genuineness of our results. Also, many existing results in the frame of metric spaces are established. Moreover, as an application, we employ the achieved result to earn the existence and uniqueness criteria of the solution of a type of non-linear integral equation.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 6
June 2023
Pages 335-343
  • Receive Date: 23 February 2021
  • Revise Date: 19 January 2023
  • Accept Date: 22 January 2023