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Mathematics 2019, 7(2), 122; https://doi.org/10.3390/math7020122

Some φ-Fixed Point Results for (F,φ,α-ψ)-Contractive Type Mappings with Applications

1
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2
Department of Applied Sciences, University Polytechnic, Aligarh Muslim University, Aligarh 202002, India
3
Department of Mathematics, Taiz University, Taiz 6803, Yemen
4
Department of Mathematics, Hajjah University, Hajjah 1729, Yemen
*
Author to whom correspondence should be addressed.
Received: 6 December 2018 / Revised: 17 January 2019 / Accepted: 18 January 2019 / Published: 23 January 2019
(This article belongs to the Section Mathematics and Computers Science)
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Abstract

In this paper, we introduce the notions of (F, φ, α- ψ)-contractions and (F, φ, α- ψ)-weak contractions in metric spaces and utilize the same to prove some existence and uniqueness φ-fixed point results. Some illustrative examples are given to demonstrate the usefulness and effectiveness of our results. As applications, we deduce some fixed point theorems in partial metric spaces besides proving an existence result on the solution of nonlinear differential equations. Our results extend, generalize and improve some relevant results of the existing literature. View Full-Text
Keywords: φ-fixed point; α-ψ-contraction mappings; (F,φ,α-ψ)-contraction mappings; (F,φ,α-ψ)-weak contraction mappings; partial metric spaces φ-fixed point; α-ψ-contraction mappings; (F,φ,α-ψ)-contraction mappings; (F,φ,α-ψ)-weak contraction mappings; partial metric spaces
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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Imdad, M.; Khan, A.R.; Saleh, H.N.; Alfaqih, W.M. Some φ-Fixed Point Results for (F,φ,α-ψ)-Contractive Type Mappings with Applications. Mathematics 2019, 7, 122.

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