Bipolar R-metric space and fixed point result

Document Type : Research Paper

Authors

Department of Mathematics, Lovely Professional University, Phagwara, 144411, India

Abstract

In this paper, we introduce the notion of Bipolar R-metric space that in a way enriches the present literature. Here, on associating a binary relation R with bipolar metric space, we obtain a fixed point result which is well supported with an illustrative example.

Keywords

[1] A. Alam and M. Imdad, Relation-theoretic contraction principle, J. Fixed Point Theory Appl. 17 (2015), 693–702.
[2] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1922), 133–181.
[3] V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9 (2004), 43–54.
[4] V. Berinde, General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J. Math. 24 (2008), 10–19.
[5] D. Gopal, M. Abbas, D.K. Patel and C. Vetro, Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation, ACTA Math. Sci. 36 (2016), 957–970.
[6] S. Khalehoghli, H. Rahimi and M. Eshaghi Gordji, R-topological spaces and SR-topological spaces with their applications, Math. Sci. 14 (2020), 249—255.
[7] S. Khalehoghli, H. Rahimi and M. Eshaghi Gordji, Fixed point theorems in R-metric spaces with applications, AIMS Math. 5 (2020), 3125–3137.
[8] A. Mutlu and U. G¨urdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl. 9 (2016), 5362–5373.
[9] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861–1869.
[10] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), Paper No. 94.
Volume 13, Issue 2
July 2022
Pages 709-712
  • Receive Date: 27 April 2021
  • Revise Date: 24 January 2022
  • Accept Date: 18 April 2022