# Various Fixed Point Theorems in Complex Valued -Metric Spaces.

The aim of this paper is to establish and prove several results on common fixed point for a pair of mappings satisfying more general contraction conditions portrayed by rational expressions having point-dependent control functions as coefficients in complex valued metric spaces.

Azam et al. (2011), introduce the notion of complex valued metric spaces and obtained common fixed point result for mappings in the context of complex valued metric spaces. Rao et al. (2013) introduce the notion of complex valued -metric spaces.

Some new fixed point theorems are established in the setting of complex valued -metric spaces. These new results improve and generalize Kang et al.’s results, the Banach contraction principle, and some well-known results in the literature. 1.

Recently, Azam et al. introduced new spaces called the complex valued metric spaces and established the existence of fixed point theorems under the contraction condition. In this article, we extend and improve the condition of contraction of the results of Azam et al. and also apply the main result to the unique common solution of system of Urysohn integral equation. Mathematics Subject.

Recently, Azam et al. first introduced the complex valued metric spaces which is more general than well-know metric spaces and also gave common fixed point theo- rems for mappings satisfying generalized contraction condition. Theorem 1.1 (Azametal.).Let (X, d) be a complete complex valued metric.

In mathematical analysis. The Banach fixed-point theorem gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point. By contrast, the Brouwer fixed-point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it.

In this paper, first we prove a common fixed point theorem for a pair of weakly compatible self maps in complex valued metric space for rational inequality. Secondly, we prove common fixed point theorems for weakly compatible mappings along with.

COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN COMPLEX VALUED METRIC SPACE Muhammad Sarwar, Mian Bahadur Zada, and Saurabh Manro Abstract. In this paper, using the (CLR) and (E:A) properties of the in-volved pairs, common xed point results for four and six weakly compatible self-mappings are established in complex valued metric.

Recently, the concept of complex valued metric spaces was introduced by Azam et al. in 2011 and further they proved some fixed point results for mappings satisfying a rational inequality. In (32), Saluja proved some fixed point theorems under rational contraction in the setting of complex valued metric spaces. Motivated by these results, in.