On some common coupled fixed point results in rectangular b-metric spaces

Abstract

In this paper, by using the w-compatible conditions of mapping pair, we discuss the existence and uniqueness problem of the common coupled fixed point for mappings defined on a set equipped with two rectangular b-metrics. Some new common coupled fixed point theorems are obtained. We also provide illustrative examples in support of our new results. As application, we provide an existence and uniqueness theorem of common solution for a class of nonlinear integral equations by using the obtained new result. The results presented in this paper generalize the well-known comparable results in the literature.

On Some Coupled Fixed Points of Generalized T-Contraction Mappings in a bv(s)-Metric Space and Its Application

“…In the present note, we have given coupled fixed point results for a pair of generalized T-contraction mappings in a b v (s)-metric space. Our results are new and it extends, generalize, and improve some of the coupled fixed point theorems recently dealt with in [10][11][12].…”

“…Remark 2. Note that condition (2.1) of Gu [10] implies (20) and hence Corollary 2 gives an improved version of Theorem 2.1 of Gu [10].…”

“…Some recent fixed point theorems in such generalized metric spaces can be found in [6][7][8][9]. In [10][11][12], one can find some interesting coupled fixed point theorems and their applications proved in some generalized forms of a metric space. In the present note, we have given coupled fixed point results for a pair of generalized T-contraction mappings in a b v (s)-metric space.…”

Fixed Point Theorems in $ b$-Rectangular Metric Spaces

“…Also, the concept of b−rectangular metric space is introduced as a generalization of b−metric space and rectangular (generalized) metric space by Geoge et al [11]. Also see [9], [10], [14] , [16], [17], [22]. [6] Let X be a nonempty set and s ≥ 1 be a given real number.…”

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.…”