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Open AccessArticle

New Fixed Point Results via (θ,ψ)R-Weak Contractions with an Application

by 1,†, 1,†, 2,*,†, 3,*,† and 4,†
1
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2
Department of Mathematics, Hajjah University, Hajjah 1729, Yemen
3
Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
4
Department of Mathematics, Prince Sattam Bin Abdulaziz University, Alkharj 11911, Saudi Arabia
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(6), 887; https://doi.org/10.3390/sym12060887
Received: 2 May 2020 / Revised: 25 May 2020 / Accepted: 26 May 2020 / Published: 30 May 2020
In this paper, inspired by Jleli and Samet (Journal of Inequalities and Applications 38 (2014) 1–8), we introduce two new classes of auxiliary functions and utilize the same to define ( θ , ψ ) R -weak contractions. Utilizing ( θ , ψ ) R -weak contractions, we prove some fixed point theorems in the setting of relational metric spaces. We employ some examples to substantiate the utility of our newly proven results. Finally, we apply one of our newly proven results to ensure the existence and uniqueness of the solution of a Volterra-type integral equation. View Full-Text
Keywords: fixed point; θ-contraction; binary relation; integral equation fixed point; θ-contraction; binary relation; integral equation
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MDPI and ACS Style

Imdad, M.; Ali, B.; Alfaqih, W.M.; Sessa, S.; Aldurayhim, A. New Fixed Point Results via (θ,ψ)R-Weak Contractions with an Application. Symmetry 2020, 12, 887.

AMA Style

Imdad M, Ali B, Alfaqih WM, Sessa S, Aldurayhim A. New Fixed Point Results via (θ,ψ)R-Weak Contractions with an Application. Symmetry. 2020; 12(6):887.

Chicago/Turabian Style

Imdad, Mohammad; Ali, Based; Alfaqih, Waleed M.; Sessa, Salvatore; Aldurayhim, Abdullah. 2020. "New Fixed Point Results via (θ,ψ)R-Weak Contractions with an Application" Symmetry 12, no. 6: 887.

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