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Open AccessArticle

A Solution of Fredholm Integral Equation by Using the Cyclic η s q -Rational Contractive Mappings Technique in b-Metric-Like Spaces

1
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
2
Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa (Bizkaia), Spain
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(9), 1184; https://doi.org/10.3390/sym11091184
Received: 26 August 2019 / Revised: 14 September 2019 / Accepted: 16 September 2019 / Published: 19 September 2019
(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)
In this article, the notion of cyclic η s q -rational contractive mappings is discussed and some fixed point theorems in the context of complete b-metric-like spaces are showed. Here, the obtained consequences unify, extend and generalize various comparable known results. Furthermore, new common fixed point outcomes in a directed graph are demonstrated. Moreover, some useful examples are discussed to justify our theoretical results and finding a solution of Fredholm integral equation was discussed as enforcement. View Full-Text
Keywords: cyclic ηsq-rational contractive mapping; a directed graph; fixed point technique; Fredholm integral equation; b-metric-like spaces cyclic ηsq-rational contractive mapping; a directed graph; fixed point technique; Fredholm integral equation; b-metric-like spaces
MDPI and ACS Style

Hammad, H.A.; De la Sen, M. A Solution of Fredholm Integral Equation by Using the Cyclic η s q -Rational Contractive Mappings Technique in b-Metric-Like Spaces. Symmetry 2019, 11, 1184.

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