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Axioms 2019, 8(1), 13; https://doi.org/10.3390/axioms8010013

Fixed Point Results in Partial Symmetric Spaces with an Application

1
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
2
Department of Applied sciences, University Polytechnic, Aligarh Muslim University, Aligarh-202002, India
*
Author to whom correspondence should be addressed.
Received: 8 December 2018 / Revised: 5 January 2019 / Accepted: 15 January 2019 / Published: 22 January 2019
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
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Abstract

In this paper, we first introduce the class of partial symmetric spaces and then prove some fixed point theorems in such spaces. We use one of the our main results to examine the existence and uniqueness of a solution for a system of Fredholm integral equations. Furthermore, we introduce an analogue of the Hausdorff metric in the context of partial symmetric spaces and utilize the same to prove an analogue of the Nadler contraction principle in such spaces. Our results extend and improve many results in the existing literature. We also give some examples exhibiting the utility of our newly established results. View Full-Text
Keywords: partial symmetric; fixed point; contraction and weak contraction; Nadler’s theorem partial symmetric; fixed point; contraction and weak contraction; Nadler’s theorem
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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Asim, M.; Khan, A.R.; Imdad, M. Fixed Point Results in Partial Symmetric Spaces with an Application. Axioms 2019, 8, 13.

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