On ordered theoretic controlled fuzzy metric spaces

Document Type : Research Paper

Authors

1 Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan

2 Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan

3 Office of Research, Innovation and Commercialization, University of Management and Technology Lahore, Pakistan

4 Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Abstract

In this article, we introduce the concept of $\Re $-control fuzzy metric spaces. We prove some fixed point results in the sense of $\Re $-control fuzzy metric spaces and furnish our work with several non-trivial examples to verify the validity of the proposed results. In the end, we incorporate this work with an application to solve an integral equation.

Keywords

[1] I. Altun and D. Mihet, Ordered non-Archidemedean fuzzy metric spaces and some fixed point results, Fixed Point Theory Appl. 2010 (2010), Article ID 782680.
[2] H. Baghani and M. Ramezani, A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat 31 (2017), 3875–3884.
[3] I.A. Bakhtin, The contraction mapping principle in quasi metric spaces, Ul’yanovsk. Gos. Ped. Inst. 30 (1989), 26–37.
[4] S. Chauhan and V. Gupta, Banach contraction theorem on fuzzy cone-metric space, J. Appl. Res. Technol. 18 (2020) , no. 4, 154–160.
[5] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Infor. Univ. Ostraviensis 1 (1993), 5–11.
[6] Z.K. Deng, Fuzzy pseudo-metric spaces, J. Math. Anal. Appl. 86 (1982), 74–95.
[7] T. Doenovi´c, A. Javaheri, S. Sedghi and N. Shobe, Coupled fixed point theorem in b-fuzzy metric spaces, Novi Sad J. Math. 47 (2017), 77–88.
[8] M. Farheen, K. Ahmed, K. Javed, V. Parvaneh, F. Ud Din and U. Ishtiaq, Intuitionistic fuzzy double controlled metric spaces and related results, Secur. Commun. Networks 2022 (2022).
[9] M. Farhan, U. Ishtiaq, M. Saeed, A. Hussain and H. Al Sulami, Reich-type and (a, F)-contractions in partially ordered double-controlled metric-type spaces with applications to non-linear fractional differential equations and monotonic iterative method, Axioms 10 (2022), 573.
[10] V. Gupta, M. Verma and J. Kaur, A new contraction and existence theorems on fuzzy metric space with a graph, Ital. J. Pure Appl. Math. 43 (2020), 717–729.
[11] K. Javed, F. Uddin, H. Aydi, A. Mukheimer and M. Arshad, Ordered-theoretic fixed point results in fuzzy b-metric spaces with an application, J. Math. 2021 (2021), Article ID 6663707.
[12] S. Khalehoghli, H. Rahimi and M. Eshaghi Gordji, Fixed point theorem in R-metric spaces with applications, AIMS Math. 5 (2020), 3125–3137.
[13] F. Mehmood, Extended fuzzy b-metric spaces, J. Math. Anal. 8 (2017), no. 6, 124–131.
[14] F. Mehmood, R. Ali, C. Ionescu and T. Kamran, Extended fuzzy b-metric spaces, J. Math. Anal. 6 (2017), 124–131.
[15] D. Mihet, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets Syst. 159 (2008), 739–744.
[16] N. Mlaiki, Controlled metric type spaces and the related contraction principle, Math. 6 (2018), Paper No. 194.
[17] D. Raki´c, A. Mukheimer, T. Doenovi´c, Z.D. Mitrovi´c and S. Radenovi´c, On some new fixed point results in fuzzy b-metrics spaces, J. Inequal. Appl. 2020 (2020), Paper No. 99.
[18] A. Rold´an, J. Mart´─▒nez-Moreno and C. Rold´an, On interrelationships between fuzzy metric structures, Iran. J. Fuzzy Syst. 10 (2013), no. 2, 133–150, 160.
[19] K. Sawangsup and W. Sintunavarat, Discussion on relation theoretic for JS-quasi contraction of uni/multidimensional mapping with the transitivity, Proyecciones 39 (2020), no. 3, 559–580.
[20] S. Sedghi and N. Shobe, Common fixed point theorem in b-fuzzy metric space, Nonlinear Funct. Anal. Appl. 17 (2012), 349–359.
[21] M.S. Sezen, Controlled fuzzy metric spaces and some related fixed point results, Numer. Meth. Partial Differ. Equ. 37 (2021), 583–593.
[22] F. Uddin, U. Ishtiaq, A. Hussain, K. Javed, H. Al Sulami and K. Ahmed, Neutrosophic double controlled metric spaces and related results with application, Fractal Fractional 6 (2022),318.
[23] L.A. Zadeh, Fuzzy sets, Inf. Control 3 (1965), 338–353.
Volume 14, Issue 4
April 2023
Pages 1-14
  • Receive Date: 20 September 2022
  • Revise Date: 28 November 2022
  • Accept Date: 23 January 2023