scholarly journals On Fredholm type integrodifferential equation

2008 ◽  
Vol 39 (1) ◽  
pp. 85-94 ◽  
Author(s):  
B. G. Pachpatte
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Integral Inequality ◽  
Banach Fixed Point Theorem ◽  
Explicit Estimate ◽  
Fredholm Type

In this paper we study the existence, uniqueness and other properties of solutions of a Fredholm type integrodifferential equation. The main tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate.

scholarly journals Implicit type Volterra integrodifferential equation

2010 ◽  
Vol 41 (1) ◽  
pp. 97-107
Author(s):  
B. G. Pachpatte
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Integral Inequality ◽  
Banach Fixed Point Theorem ◽  
Explicit Estimate ◽  
Volterra Integrodifferential Equation

In this paper we study the existence, uniqueness and other properties of solutions of a certain nonlinear implicit type Volterra integrodifferential equation. The Banach fixed point theorem and a certain integral inequality with explicit estimate are used to establish the results.

scholarly journals Properties of Some Partial Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Deepak B. Pachpatte
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Integral Inequality ◽  
Dynamic Equation ◽  
Dynamic Equations ◽  
Banach Fixed Point Theorem

The main objective of the paper is to study the properties of the solution of a certain partial dynamic equation on time scales. The tools employed are based on the application of the Banach fixed-point theorem and a certain integral inequality with explicit estimates on time scales.

Controllability of mixed Volterra–Fredholm type integrodifferential third order dispersion equations

2015 ◽  
Vol 21 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Mohit Kumar ◽  
Nagarajan Sukavanam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Dispersion Equation ◽  
Point Theorem ◽  
Banach Fixed Point Theorem ◽  
Third Order ◽  
Fredholm Type ◽  
Strongly Continuous Semigroups ◽  
Third Order Dispersion ◽  
Order Dispersion

AbstractIn this paper, we establish a result concerning the controllability of a mixed Volterra–Fredholm type integrodifferential third order dispersion equation. The result is obtained by using the theory of strongly continuous semigroups and the Banach fixed point theorem.

scholarly journals Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions

2017 ◽  
Vol 4 (1) ◽  
pp. 1-15
Author(s):  
Machindra B. Dhakne ◽  
Poonam S. Bora
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Strong Solutions ◽  
Fractional Power Of Operators

Abstract In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

scholarly journals Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

2020 ◽  
Vol 19 (1) ◽  
pp. 171-192
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

Maia-Perov type fixed point results for Presic type operators

2017 ◽  
Vol 33 (3) ◽  
pp. 265-274
Author(s):  
MARGARETA-ELIZA BALAZS ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Basic Problem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fredholm Type ◽  
System Of Integral Equations

Starting from the results, established in [Albu, M., A fixed point theorem of Maia-Perov type. Studia Univ. Babes¸- Bolyai Math., 23 (1978), No. 1, 76–79] and [Mures¸an, V., Basic problem for Maia-Perov’s fixed point theorem, Seminar on Fixed Point Theory, Babes¸ Bolyai Univ., Cluj-Napoca, (1988), Preprint Nr. 3, pp. 43–48] where fixed point theorems of Maia-Perov type are proved, the main aim of this paper is to extend this results to product metric spaces, using Presiˇ c type operators. An existence, uniqueness and data dependence theorem related to the ´ solution of the system of integral equations of Fredholm type in product metric spaces, is also presented.

Sign in / Sign up

Export Citation Format

Share Document