Abstract
Objectives/Aim: To find fixed points for integral types of contraction mappings in a complex valued metric spaces. Methods: We used mathmatical analysis to prove the results as a generalization of weakly contraction self mappings defined in a complex metric space. Findings: We are finding by weakly integral types of contraction self mappings that there are common fixed points. In this paper we used commutative self mappings for our conclusions . Application/ Improvements: In future it can also be used for the exestense and uniquence of the differential equations solutions. Keywords: Complex Valued Metric Space, Contraction Mapping, Fixed Point, Integral Type, Weakly Commuting
Highlights
A fixed point theory contains a great number of generalizations of Banach contraction principle by using different form of contraction condition in various spaces
Majority of such generalizations are obtained by improving underlying contraction conditions which includes contraction conditions dscribed by rational expressions
In this study we present a common fixed point result for two self-mappings satisfying a contractive condition in complex valued metric spaces .This idea is intended to define rational expressions which are not meaningful in cone metric spaces and many such results of analysis cannot be generalized to cone metric spaces but to complex valued metric spaces
Summary
A fixed point theory contains a great number of generalizations of Banach contraction principle by using different form of contraction condition in various spaces. In this study we present a common fixed point result for two self-mappings satisfying a contractive condition in complex valued metric spaces .This idea is intended to define rational expressions which are not meaningful in cone metric spaces and many such results of analysis cannot be generalized to cone metric spaces but to complex valued metric spaces. Let (X;d) be a complex valued metric space, xn be a sequence in X and x ∈ X .
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