Some Fixed Point Theorems in Complex Valued b-Metric Spaces

Abstract

Recently, Azam et al. introduced the notion of complex valued metric spaces and proved fixed point theorems under the contraction condition. Rao et al. introduced the notion of complex valued b-metric spaces. In this paper, we obtain some fixed point results for the mapping satisfying rational expressions in complex valued b-metric spaces. Also, an example is given to illustrate our obtained result.

Fixed Point Theorems in Complex Valued B-Metric Spaces

“…Based on the definition of partial order on complex numbers, real-valued b-metric can be generalized into complex-valued b-metric as follows. Definition 3 (see [13]). Let be a nonempty set and let ≥ 1 be a given real number.…”

“…Fixed point theorems in metric spaces have been studied extensively by many researchers as in [1], [2], and [3]. After Bakhtin [4] introduced the notion of b-metric spaces in 1989, researchers started to develop fixed point theorems in the spaces, for example in [5], [6], and [7]. In 2011, Azzam et.…”

Iterated Function Systems Consisting of Generalized Convex Contractions in the Framework of Complete Strong b-metric Spaces

“…A. Bakhtin (see [8]) and S. Czerwik (see [15] and [16]). In the last years a lot of fixed point results in the framework of b-metric spaces have been obtained (see, for example, [1], [7], [9], [11], [12], [17], [27], [28], [29], [31], [40], [41], [42], [44], [46], [47], [49], [50], [51], [55], [56] and [59]). …”

FIXED POINT THEOREMS USING (CLCS) PROPERTY IN COMPLEX VALUED $b$-METRIC SPACES

“…Recently, Mukheimer [27], Rao et al [35], Dubey et al [14] and Singh et al ( [46], [47]) etc. proved some common fixed point results in complex valued b-metric spaces.…”