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Symmetry 2018, 10(12), 732; https://doi.org/10.3390/sym10120732 (registering DOI)

Unification of the Fixed Point in Integral Type Metric Spaces

1
Department of Mathematics, Basic Sciences and Humanities, GMR Institute of Technology, GMR Nagar, Rajam, Srikakulam Dist., Andhra Pradesh 532127, India
2
Department of Mathematics, King Abdulaziz University P.O. Box 80203, Jeddah 21589, Saudi Arabia
3
School of Mathematics, Thapar Institute of Engineering & Technology (Deemed to be University), Patiala 147004, Punjab, India
*
Authors to whom correspondence should be addressed.
Received: 13 November 2018 / Revised: 29 November 2018 / Accepted: 4 December 2018 / Published: 7 December 2018
PDF [299 KB, uploaded 7 December 2018]

Abstract

In metric fixed point theory, the conditions like “symmetry” and “triangle inequality” play a predominant role. In this paper, we introduce a new kind of metric space by using symmetry, triangle inequality, and other conditions like self-distances are zero. In this paper, we introduce the weaker forms of integral type metric spaces, thereby we establish the existence of unique fixed point theorems. As usual, illustrations and counter examples are provided wherever necessary.
Keywords: weaker forms of generating spaces; weaker forms of integral type metric spaces; cyclic map weaker forms of generating spaces; weaker forms of integral type metric spaces; cyclic map
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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Kumari, P.S.; Alamri, B.A.S.; Hussain, N.; Chandok, S. Unification of the Fixed Point in Integral Type Metric Spaces. Symmetry 2018, 10, 732.

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