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Mathematics 2019, 7(2), 194; https://doi.org/10.3390/math7020194

Common Fixed Point Theorems of Generalized Multivalued (ψ,ϕ)-Contractions in Complete Metric Spaces with Application

1
Department of Mathematics, Taiz University, Taiz, Yemen
2
Department of Mathematics, International Islamic University, H-10, Islamabad 44000, Pakistan
3
Department of Mathematics, University of Seoul, Seoul 02504, Korea
4
Department of Financial Mathematics, Hanshin University, Gyeonggi-do 18101, Korea
*
Author to whom correspondence should be addressed.
Received: 18 January 2019 / Revised: 3 February 2019 / Accepted: 17 February 2019 / Published: 18 February 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
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Abstract

The purpose of this paper is to introduce the notion of generalized multivalued ψ , ϕ-type contractions and generalized multivalued ψ , ϕ-type Suzuki contractions and establish some new common fixed point theorems for such multivalued mappings in complete metric spaces. Our results are extension and improvement of the Suzuki and Nadler contraction theorems, Jleli and Samet, Piri and Kumam, Mizoguchi and Takahashi, and Liu et al. fixed point theorems. We provide an example for supporting our new results. Moreover, an application of our main result to the existence of solution of system of functional equations is also presented. View Full-Text
Keywords: fixed point; generalized multivalued (ψ,ϕ)-type contraction; generalized multivalued (ψ,ϕ)-type Suzuki contraction fixed point; generalized multivalued (ψ,ϕ)-type contraction; generalized multivalued (ψ,ϕ)-type Suzuki contraction
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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Ameer, E.; Arshad, M.; Shin, D.Y.; Yun, S. Common Fixed Point Theorems of Generalized Multivalued (ψ,ϕ)-Contractions in Complete Metric Spaces with Application. Mathematics 2019, 7, 194.

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