Meir-Keeler theorem in b-rectangular metric spaces

Abstract

In this paper, we prove a Meir-Keeler theorem in b-rectangular metric spaces. Thus, we answer the open question raised by Ding et al. [H. S.

A unified common fixed point theorem for a family of mappings

“…Our work provides a possibility to extend our proved results in other generalized metric spaces, namely, b−metric space, b−rectangular metric space, b ν (s)− metric spaces[2,3,9,14,15,19,33,[45][46][47][48]78].…”

Sehgal–Guseman-Type Fixed Point Theorem in b-Rectangular Metric Spaces

“…Several authors have defined different contractive mappings for b-rectangular metric spaces and discussed the fixed point theory on them (for details, see [9,13,14] and the references therein).…”

“…In the end of [7], the authors raised several open questions, one of which is whether analogues of the Chatterjee contraction, Reich contraction, Ciric contraction and Hardy-Rogers contraction theorems can be proven in b-rectangular metric spaces. Some other fixed point theorems in b-rectangular metric spaces can be seen [8,9]. In 2018, Mitrović [10] relaxed the contraction coefficient in the Banach contraction principle from k ∈ (0, 1 s ) to k ∈ (0, 1) in a b-rectangular metric space.…”

Common Fixed Point Theorem for Ciric Type Quasi-Contractions in Rectangular b-Metric Spaces

“…In [1], George et al introduced the concept of rectangular b-metric spaces as a generalization of metric space, rectangular metric space and b-metric space (see also [2,3]). Since then many fixed point theorems for various contractions were established in rectangular b-metric spaces (see [4][5][6][7][8][9][10][11][12]). Definition 1.1.…”