Common coupled fixed point theorem on fuzzy bipolar metric spaces

Document Type : Research Paper

Authors

1 Department of Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan

2 Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Kanchipuram, Chennai, Tamil Nadu, India

3 Department of Mathematics, Saveetha School of Engineering, Saveetha University, Chennai 602 105, India

Abstract

We prove a common coupled fixed point theorem on fuzzy bipolar metric spaces. An application of our key results is given to solve a system of integral equations. Our results generalize and expand the literature’s well-known results.

Keywords

[1] S. Agnihotri, K.K. Dubey and V.K. Gupta, Common fixed point theorems in fuzzy metric space, Int. J. Appl. Engin. Res. 14 (2019), no. 11, 2738–2747.
[2] A. Azam, M. Arshad and I. Beg, Fixed points of fuzzy contractive and fuzzy locally contractive maps, Chaos Solitons Fractals 42 (2009), no. 5, 2836–2841.
[3] A. Azam and I. Beg, Common fixed points of fuzzy maps, Math. Comput. Model. 49 (2009), 1331–1336.
[4] A. Bartwal, R.C. Dimri and G. Prasad, Some fixed point theorems in fuzzy bipolar metric spaces, J. Nonlinear Sci. Appl. 13 (2020), 196–204.
[5] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994), 395–399.
[6] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 27 (1988), 385–389.
[7] V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets Syst. 125 (2002), 245–252.
[8] G.N.V. Kishore, D. Ram Prasad, B. Srinuvasa Rao and V. S. Baghavan, Some applications via common coupled fixed point theoems in bipolar metric spaces, J. Critic. Rev. 7 (2020), 601–607.
[9] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326–334.
[10] G. Mani, A.J. Gnanaprakasam, A. Ul Haq, I.A. Baloch and F. Jarad, Coupled fixed point theorems on C ∗ -algebra valued bipolar metric spaces, AIMS Math. 7 (2022), no. 5, 7552–7568.
[11] P.P. Murthy, Z.D. Mitrovic, C.P. Dhuri and S. Radenovic, The common fixed points in a bipolar metric space, Gulf J. Math. 12 (2022), no. 2, 31–38.
[12] A. Mutlu and U. Gurdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl. 9 (2016), 5362–5373.
[13] A. Mutlu, K. Ozkan and U. Gurdal, Coupled fixed point theorems on bipolar metric spaces, Eur. J. Pure App. Math., 10 (2017), no. 4, 655–667.
[14] B. Srinuvasa Rao and G.N.V. Kishore, Common fixed point theorems in bipolar metric spaces with applications to integral equations, Int. J. Engin. Techno. 7 (2018), 1022–1026.
[15] B. Srinuvasa Rao, G.N.V. Kishore and G. Kiran Kumar, Geraghty type contraction and common coupled fixed point theorems in bipolar metric spaces with applications to homotopy, Int. J. Math. Trends Technol. 63 (2018), 25–34.
[16] L.A. Zadeh, Fuzzy sets, Inf. Control 8 (1965), 338–353.
[17] Z. Zararsız and M. Riaz, Bipolar fuzzy metric spaces with application, Comput. Appl. Math.41 (2022), Article number 449.
Volume 14, Issue 4
April 2023
Pages 77-85
  • Receive Date: 12 July 2022
  • Accept Date: 11 February 2023