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Common Fixed Point Results of Set Valued Maps for Aφ-Contraction and Generalized ϕ-Type Weak Contraction

1
Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli, Arunachal Pradesh 791109, India
2
Department of Mathematics, Statistics and Physics, Qatar University, Doha P.O. Box 2713, Qatar
3
Department of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam 788011, India
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 894; https://doi.org/10.3390/sym11070894
Received: 9 June 2019 / Revised: 3 July 2019 / Accepted: 4 July 2019 / Published: 8 July 2019
(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)
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Abstract

The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form f ( x ) = x . One such example is that of the famous Borsuk–Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an A φ -contraction and a generalized ϕ -type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results. View Full-Text
Keywords: common fixed point; Aφ-contraction; generalized ϕ-type weak contraction; common property (EA) common fixed point; Aφ-contraction; generalized ϕ-type weak contraction; common property (EA)
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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Neog, M.; Jaradat, M.M.M.; Debnath, P. Common Fixed Point Results of Set Valued Maps for Aφ-Contraction and Generalized ϕ-Type Weak Contraction. Symmetry 2019, 11, 894.

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