Analytical Solution of Urysohn Integral Equations by Fixed Point Technique in Complex Valued Metric Spaces

Abstract

The purpose of this article is to introduce a fixed point result for a general contractive condition in the context of complex valued metric spaces. Also, some important corollaries under this contractive condition are obtained. As an application, we find a unique solution for Urysohn integral equations, and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. Previous known related results in the literarure and some other known results in the literature.

Exciting Fixed Point Results on a Novel Space with Supportive Applications

“…In Theorem 1 (i) when ϖ = 0,κ μ = s > 1 and Θ = Ξ, we have the work of Ege [17] in complex valued rectangular b-metric spaces, where ζ ∈ ½0, 1/s (ii) when κ = μ = 1 and Θ = Ξ, we have the exciting results of Azam [1] in complex valued metric spaces (iii) if we reduce a complete υ ℂ -metric space to a complete complex valued b-metric space with sζ + ϖ < 1 , we get directly the work of Mukheimer [13] (iv) when κ = μ = 1 and ζ, ϖ : ℂ + → ½0,1Þ are two mappings in a complete complex valued metric space, we have the results of Sintunavarat et al [5] In Theorem 2 (i) if we reduce a complete υ ℂ -metric space to a complete complex valued metric space with α ∈ ð0, 1Þ and κ = μ = 1, we obtain the results of Hammad [6] (ii) the conclusion of Theorems 1 and 2 is still valid by using one of the following contractive conditions:…”

“…Later, Al-Mezel et al [2] emphasized that this space is just a particular case of cone metric spaces [3,4]. Several fixed point results have been investigated on complex valued metric spaces; see [5][6][7][8][9]. The notion of a b-metric space, as a generalization of metric spaces, was introduced by Bakhtin [10] and Czerwik [11].…”

Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations via Common Fixed-Point Techniques in Complex Valued Fuzzy Metric Spaces

“…In our work, we extend fixed-point results under the general contractive condition in [25] to the setting of complex valued fuzzy metric spaces. Moreover, we studied a result of existence and uniqueness of the solution of nonlinear impulsive fractional differential equations.…”

Control Functions in G-Metric Spaces: Novel Methods for θ-Fixed Points and θ-Fixed Circles with an Application

“…As a new method of generalizing the FP theorem, Özgür and Taş [21] developed the fixed circle problem in a metric space and the concept of a fixed circle. We encourage readers to [22][23][24][25][26][27] for some recent research on the fixed-circle and fixed-disc problems.…”