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

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 852 ◽  
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Analytical Solution ◽  
Unique Solution ◽  
Integral Equations ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Fixed Point Result ◽  
Urysohn Integral Equations ◽  
Fixed Point Technique ◽  
Complex Valued

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.

scholarly journals FIXED POINT RESULTS IN COMPLEX VALUED METRIC SPACES WITH AN APPLICATION

2021 ◽  
pp. 237
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
Liliana Guran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Unique Solution ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Urysohn Integral Equations ◽  
Complex Valued

In this paper, we introduce fixed point theorem for a general contractive condition in complex valued metric spaces. Also, some important corollaries under this contractive condition areobtained. 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. [2] and some other known results in the literature.

scholarly journals Common fixed point results in complex valued metric spaces with application to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1363-1380 ◽  
Author(s):  
N. Hussain ◽  
Akbar Azam ◽  
Jamshaid Ahmad ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complex Valued Metric Space ◽  
Complex Valued

In this paper, common fixed point of six mappings satisfying a contractive condition involving rational inequality in the framework of complex valued metric space are obtained. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.

scholarly journals Generalized Common Fixed Point Results with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Marwan Amin Kutbi ◽  
Muhammad Arshad ◽  
Jamshaid Ahmad ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence Theorem ◽  
Integral Equations ◽  
Metric Spaces ◽  
Common Solution ◽  
Urysohn Integral Equations ◽  
The Common ◽  
Complex Valued

We obtained some generalized common fixed point results in the context of complex valued metric spaces. Moreover, we proved an existence theorem for the common solution for two Urysohn integral equations. Examples are presented to support our results.

scholarly journals Wardowski’s Contraction and Fixed Point Technique for Solving Systems of Functional and Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Hasanen A. Hammad ◽  
Monica-Felicia Bota ◽  
Liliana Guran
Keyword(s):  
Fixed Point ◽  
Unique Solution ◽  
Integral Equations ◽  
Directed Graph ◽  
Metric Spaces ◽  
Tripled Fixed Point ◽  
Complete Metric Spaces ◽  
Fixed Point Technique ◽  
Theoretical Results

In this manuscript, some tripled fixed point results are presented in the framework of complete metric spaces. Furthermore, Wardowski’s contraction was mainly applied to discuss some theoretical results with and without a directed graph under suitable assertions. Moreover, some consequences and supportive examples are derived to strengthen the main results. In the last part of the paper, the obtained theoretical results are used to find a unique solution to a system of functional and integral equations.

scholarly journals On Complex-Valued Triple Controlled Metric Spaces and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Nabil Mlaiki ◽  
Thabet Abdeljawad ◽  
Wasfi Shatanawi ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Polynomial Equations ◽  
Degree Polynomial ◽  
Fredholm Type ◽  
Type Integral ◽  
Type Spaces ◽  
Complex Valued

In this manuscript, we introduce the concept of complex-valued triple controlled metric spaces as an extension of rectangular metric type spaces. To validate our hypotheses and to show the usability of the Banach and Kannan fixed point results discussed herein, we present an application on Fredholm-type integral equations and an application on higher degree polynomial equations.

Existence of unique solution to nonlinear mixed Volterra Fredholm-Hammerstein integral equations in complex-valued fuzzy metric spaces

2020 ◽  
pp. 1-10
Author(s):  
Humaira ◽  
Muhammad Sarwar ◽  
Thabet Abdeljawad
Keyword(s):  
Unique Solution ◽  
Metric Spaces ◽  
General Setting ◽  
Continuous Functions ◽  
Contractive Condition ◽  
Nonlinear Functions ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Hammerstein Integral Equations ◽  
Complex Valued

The purpose of this article is to investigate the existence of unique solution for the following mixed nonlinear Volterra Fredholm-Hammerstein integral equation considered in complex plane; (0.1) ξ ( τ ) = g ( t ) + ρ ∫ 0 τ K 1 ( τ , ℘ ) ϝ 1 ( ℘ , ξ ( ℘ ) ) d ℘ + ϱ ∫ 0 1 K 2 ( τ , ℘ ) ϝ 2 ( ℘ , ξ ( ℘ ) ) d ℘ , such that ξ = ξ 1 + ξ 2 , ξ 1 , ξ 2 ∈ ( C ( [ 0 , 1 ] ) , R ) g = g 1 + g 2 , g l : [ 0 , 1 ] → R , l = 1 , 2 , ϝ l ( ℘ , ξ ( ℘ ) ) = ϝ l 1 * ( ℘ , ξ 1 * ) + i ϝ l 2 * ( ℘ , ξ 2 * ) , ϝ lj * : [ 0 , 1 ] × R → R for l , j = 1 , 2 , and ξ 1 * , ξ 2 * ∈ ( C ( [ 0 , 1 ] ) , R ) K l ( t , ℘ ) = K l 1 * ( t , ℘ ) + iK l 2 * ( t , ℘ ) , for l , j = 1 , 2 and K lj * : [ 0 , 1 ] 2 → R , where ρ and ϱ are constants, g (t), the kernels K l  (τ, ℘) and the nonlinear functions ϝ1 (℘ , ξ (℘)) , ϝ 2 (℘ , ξ (℘)) are continuous functions on the interval 0 ≤ τ ≤ 1. In this direction we apply fixed point results for self mappings with the concept of (ψ, ϕ) contractive condition in the setting of complex-valued fuzzy metric spaces. This study will be useful in the development of the theory of fuzzy fractional differential equations in a more general setting.

scholarly journals Weakly compatible maps in complex valued metric spaces and an application to solve Urysohn integral equation

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2695-2709
Author(s):  
Manoj Kumar ◽  
Pankaj Kumar ◽  
Sanjay Kumar ◽  
Serkan Araci
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Maps ◽  
Weakly Compatible Maps ◽  
Weakly Compatible ◽  
Urysohn Integral Equations ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper, we prove common fixed point theorems for a pair of mappings satisfying rational inequality. Also, we prove common fixed point theorems for weakly compatible maps, weakly compatible along with (CLR) and E.A. properties that generalizes the results of Sintunavarat et al. [15]. Further, we apply our results to find the solution of Urysohn integral equations x(t) = ?b,a K1(t,s,x(s))ds + g(t), x(t) = ?b,a K2(t,s,x(s))ds + h(t), where t ? [a,b]? R,x,g,h ? X and K1,K2: [a,b] x [a,b] x Rn ? Rn.

scholarly journals Multi-valued F-contractions and the solutions of certain functional and integral equations

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1259-1268 ◽  
Author(s):  
Margherita Sgroi ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Banach Contraction

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

scholarly journals Unified common fixed point theorems in complex valued metric spaces via an implicit relation with applications

2019 ◽  
Vol 38 (4) ◽  
pp. 9-29
Author(s):  
Waleed Mohd Alfaqih ◽  
Mohammad Imdad ◽  
Fayyaz Rouzkard
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Implicit Relation ◽  
Common Solution ◽  
Weakly Compatible ◽  
Urysohn Integral Equations ◽  
Complex Valued ◽  
Common Fixed Point Theorems

The purpose of this paper is to prove some common fixed point theorems for two pairs of weakly compatible mappings in complex valued metric spaces satisfying an implicit relation. Several illustrative examples are given which demonstrate the usefulness of our utilized implicit relation. Beside generalizing and improving several well known core results of the existing literature we can deduce several new contractions which have not obtained before in complex valued metric spaces. As an application of our results, we prove the existence and uniqueness of common solution of Hammerstein as well as Urysohn integral equations.

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