scholarly journals On Fredholm type integral equation in two variables

2009 ◽  
pp. 27-39 ◽  
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Equation ◽  
Fredholm Type ◽  
Type Integral

scholarly journals New Explicit Bounds on Gamidov Type Integral Inequalities for Functions in Two Variables and Their Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Kelong Cheng ◽  
Chunxiang Guo
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Integral Inequalities ◽  
Fredholm Integral Equations ◽  
Uniqueness Of Solutions ◽  
Fredholm Type ◽  
Type Integral ◽  
Explicit Bounds ◽  
Linear And Nonlinear

Some linear and nonlinear Gamidov type integral inequalities in two variables are established, which can give the explicit bounds on the solutions to a class of Volterra-Fredholm integral equations. Some examples of application are presented to show boundedness and uniqueness of solutions of a Volterra-Fredholm type integral equation.

scholarly journals On the Solutions of a Class of Integral Equations Pertaining to Incomplete H-Function and Incomplete H-Function

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 819
Author(s):  
Manish Kumar Bansal ◽  
Devendra Kumar ◽  
Jagdev Singh ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Integral Equation ◽  
Fractional Calculus ◽  
Integral Equations ◽  
Real World ◽  
Mellin Transform ◽  
Fredholm Type ◽  
Type Integral ◽  
Real World Problems

The main aim of this article is to study the Fredholm-type integral equation involving the incomplete H-function (IHF) and incomplete H-function in the kernel. Firstly, we solve an integral equation associated with the IHF with the aid of the theory of fractional calculus and Mellin transform. Next, we examine an integral equation pertaining to the incomplete H-function with the help of theory of fractional calculus and Mellin transform. Further, we indicate some known results by specializing the parameters of IHF and incomplete H-function. The results computed in this article are very general in nature and capable of giving many new and known results connected with integral equations and their solutions hitherto scattered in the literature. The derived results are very useful in solving various real world problems.

scholarly journals Fixed points of $(\psi, \phi)-$contractions and Fredholm type integral equation

2021 ◽  
Vol 2 (1) ◽  
pp. 91-100
Author(s):  
Nabil Mlaiki ◽  
Doaa Rizk ◽  
Fatima Azmi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Spaces ◽  
Fredholm Type ◽  
Contractive Mappings ◽  
Type Integral

In this paper, we establish a fixed point theorem for controlled rectangular $b-$metric spaces for mappings that satisfy $(\psi, \phi)-$contractive mappings. Also, we give an application of our results as an integral equation.

scholarly journals On certain methods of solving a class of integral equations of Fredholm type

1992 ◽  
Vol 52 (1) ◽  
pp. 1-10 ◽  
Author(s):  
H. M. Srivastava ◽  
R. K. Raina
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Mellin Transform ◽  
Integral Transforms ◽  
Fredholm Type ◽  
Reduction Techniques ◽  
Hypergeometric Integral ◽  
Type Integral ◽  
Interesting Generalization

AbstractThe authors begin by presenting a brief survey of the various useful methods of solving certain integral equations of Fredholm type. In particular, they apply the reduction techniques with a view to inverting a class of generalized hypergeometric integral transforms. This is observed to lead to an interesting generalization of the work of E. R. Love [9]. The Mellin transform technique for solving a general Fredholm type integral equation with the familiar H-function in the kernel is also considered.

scholarly journals Kannan-Type Contractions on New Extended b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hassen Aydi ◽  
Muhammad Aslam ◽  
Dur-e-Shehwar Sagheer ◽  
Samina Batul ◽  
Rashid Ali ◽  
...  
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Asymptotic Regularity ◽  
Existence Of A Solution ◽  
Fredholm Type ◽  
Type Integral

This article is focused on the generalization of some fixed point theorems with Kannan-type contractions in the setting of new extended b -metric spaces. An idea of asymptotic regularity has been incorporated to achieve the new results. As an application, the existence of a solution of the Fredholm-type integral equation is presented.

scholarly journals Fredholm-type integral equation in controlled metric-like spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wasfi Shatanawi ◽  
Nabil Mlaiki ◽  
Doaa Rizk ◽  
Enyinda Onunwor
Keyword(s):  
Integral Equation ◽  
Fredholm Type ◽  
Banach Contraction ◽  
Type Integral

AbstractIn this article we make an improvement in the Banach contraction using a controlled function in controlled metric like spaces, which generalizes many results in the literature. Moreover, we present an application on Fredholm type integral equation.

scholarly journals Fredholm type integral equation in extended $M_{b}$-metric spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Nabil Mlaiki ◽  
Mohamed Hajji ◽  
Thabet Abdeljawad
Keyword(s):  
Integral Equation ◽  
Metric Spaces ◽  
Fredholm Type ◽  
Type Integral

scholarly journals Ordered-Theoretic Fixed Point Results in Fuzzy b-Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalil Javed ◽  
Fahim Uddin ◽  
Hassen Aydi ◽  
Aiman Mukheimer ◽  
Muhammad Arshad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fredholm Type ◽  
Banach Contraction ◽  
Type Integral

The aim of this manuscript is to initiate the study of the Banach contraction in R-fuzzy b-metric spaces and discuss some related fixed point results to ensure the existence and uniqueness of a fixed point. A nontrivial example is imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the provided results, an application is presented to solve the first kind of a Fredholm-type integral equation.

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