Addressing an open problem of Choudhury et al. “Fuzzy Sets Syst. 8 (2013), 84-97”

Subtitle: (In the sacred memory of Manish Jain’s mother: Smt. Shashi Jain (05-06-1953 to 21-01-2020))

Article type: Research Article

Authors: Jain, Manish^{a; *} | Kumar, Sanjay^b | Park, Choonkil^{c; *}

Affiliations: [a] Department of Mathematics, Ahir College, Rewari, India | [b] Department of Mathematics, DCRUST, Murthal, Sonepat, India | [c] Research Institute for Natural Sciences, Hanyang University, Seoul, Korea

Correspondence: [*] Corresponding authors. Choonkil Park (Email: [email protected], Fax: +82 2 2281 0019), Manish Jain (Email: [email protected]).

Abstract: The question of relaxing the compatible hypothesis of the pair of mappings in fixed point theory has always been remained an open problem. We address such an open problem raised by Choudhury et al. [4] and also explicitly settles the issue of monotone and continuity hypotheses of the involved mappings in coupled coincidence point results. Moreover, we state a gap in an example given in [3] and repair it. Application to the dynamic programming problem shows the usability of present work. Finally, we also propose an open problem for further investigation.

Keywords: GV-fuzzy metric space,φ-contractions, Hadɘić type t-norm, mixed monotone property, coupled coincidence point 2010 Mathematics Subject Classification. 47H10, 54H25.

DOI: 10.3233/JIFS-222637

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 5, pp. 7211-7223, 2023