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Symmetry 2019, 11(2), 206; https://doi.org/10.3390/sym11020206

A New Approach to the Solution of Non-Linear Integral Equations via Various FBe-Contractions

1
Department of Mathematics, Basic Sciences and Humanities, GMR Institute of Technology, Rajam 532127, Andhra Pradesh, India
2
College of Computer and Information Sciences, Majmaah University, Majmaah 11952, Saudi Arabia
3
Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
4
Distinguished University Professor of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA
*
Authors to whom correspondence should be addressed.
Received: 8 January 2019 / Revised: 23 January 2019 / Accepted: 28 January 2019 / Published: 12 February 2019
(This article belongs to the Special Issue Nonlinear, Convex, Nonsmooth, Functional Analysis in Symmetry)
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Abstract

In this article, we introduce and establish various approaches related to the F-contraction using new sorts of contractions, namely the extended F B e -contraction, the extended F B e -expanding contraction, and the extended generalized F B e -contraction. Thereafter, we propose a simple and efficient solution for non-linear integral equations using the fixed point technique in the setting of a B e -metric space. Moreover, to address conceptual depth within this approach, we supply illustrative examples where necessary. View Full-Text
Keywords: extended b-metric space; extended ℱBe-contraction; extended FBe-expanding contraction; extended weak generalized FBe-contraction; non-linear integral equation extended b-metric space; extended ℱBe-contraction; extended FBe-expanding contraction; extended weak generalized FBe-contraction; non-linear integral equation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Panda, S.K.; Tassaddiq, A.; Agarwal, R.P. A New Approach to the Solution of Non-Linear Integral Equations via Various FBe-Contractions. Symmetry 2019, 11, 206.

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