On Solvability of the Integro-Differential Equations

2022 ◽  
Vol 27 (1) ◽  
pp. 1-9
Author(s):  
Faez Ghaffoori
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Point Theorem ◽  
Integral Functional ◽  
Existence Of Solution ◽  
Bounded Interval ◽  
The Fixed Point Theorem

In this paper, we study the existence of solution to integro-differential equations in the space of Lebesgue-integrable  on un-bounded interval after transformed to nonlinear integral functional equation, the used tool is the fixed point theorem due to Schauder with weak measure of non compactness, due to De-Blasi. In addition, we give an example which satisfies the conditions of our existence theorem.

Existence on solutions of a class of casual differential equations on a time scale

2021 ◽  
Vol 71 (3) ◽  
pp. 683-696
Author(s):  
Yige Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Algebra ◽  
Existence Theorem ◽  
Point Theorem ◽  
Comparison Principle ◽  
Time Scale ◽  
Differential Inequalities ◽  
The Fixed Point Theorem

Abstract In this paper, we develop the theory of a class of casual differential equations on a time scale. An existence theorem for casual differential equations on a time scale is given under mixed Lipschitz and compactness conditions by the fixed point theorem in Banach algebra due to Dhage. Some fundamental differential inequalities on a time scale are also presented which are utilized to investigate the existence of extremal solutions. The comparison principle on casual differential equations on a time scale is established. Our results in this paper extend and improve some well-known results.

scholarly journals The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

scholarly journals Existence solution of a system of differential equations using generalized Darbo's fixed point theorem

2021 ◽  
Vol 6 (12) ◽  
pp. 13358-13369
Author(s):  
Rahul ◽  
◽  
Nihar Kumar Mahato
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solution ◽  
System Of Differential Equations ◽  
Darbo’S Fixed Point Theorem ◽  
Darbo Fixed Point Theorem

<abstract><p>In this paper, we proposed a generalized of Darbo's fixed point theorem via the concept of operators $ S(\bullet; .) $ associated with the measure of noncompactness. Using this generalized Darbo fixed point theorem, we have given the existence of solution of a system of differential equations. At the end, we have given an example which supports our findings.</p></abstract>

scholarly journals Existence of solutions of nonlinear differential equations with deviating arguments

1991 ◽  
Vol 44 (3) ◽  
pp. 467-476
Author(s):  
K. Balachandran ◽  
S. Ilamaran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.

scholarly journals Brzdęk’s fixed point method for the generalised hyperstability of bi-Jensen functional equation in (2,β)-Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4897-4910
Author(s):  
Iz-Iddine El-Fassi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Point Method ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
The Fixed Point Theorem

Using the fixed point theorem [12, Theorem 1] in (2,?)-Banach spaces, we prove the generalized hyperstability results of the bi-Jensen functional equation 4f(x + z/2; y + w/2) = f (x,y) + f (x,w) + f (z,y) + f (y,w). Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. The method we use here can be applied to various similar equations in many variables.

Extensions of Perov theorem

2015 ◽  
Vol 31 (2) ◽  
pp. 181-188
Author(s):  
MARIJA CVETKOVIC ◽  
◽  
VLADIMIR RAKOCEVIC ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Integral Functional ◽  
Generalized Metric Space ◽  
The Fixed Point Theorem ◽  
Vector Valued ◽  
Banach’S Contraction Principle ◽  
Cone Metric

[Perov, A. I., On Cauchy problem for a system of ordinary diferential equations, (in Russian), Priblizhen. Metody Reshen. Difer. Uravn., 2 (1964), 115-134] used the concept of vector valued metric space and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article we study fixed point results for the new extensions of Banach’s contraction principle to cone metric space, and we give some generalized versions of the fixed point theorem of Perov. As corollaries some results of [Zima, M., A certain fixed point theorem and its applications to integral-functional equations, Bull. Austral. Math. Soc., 46 (1992), 179–186] and [Borkowski, M., Bugajewski, D. and Zima, M., On some fixed-point theorems for generalized contractions and their perturbations, J. Math. Anal. Appl., 367 (2010), 464–475] are generalized for a Banach cone space with a non-normal cone. The theory is illustrated with some examples.

scholarly journals The Stability of a General Sextic Functional Equation by Fixed Point Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jaiok Roh ◽  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Fixed Point Theorem ◽  
The Stability

In this paper, we will consider the generalized sextic functional equation ∑ i = 0 7   7 C i − 1 7 − i f x + i y = 0 . And by applying the fixed point theorem in the sense of C a ˘ dariu and Radu, we will discuss the stability of the solutions for this functional equation.

scholarly journals A study of fractional integro-differential equations via Hilfer-Hadamard fractional derivative

2019 ◽  
Vol 27 (1) ◽  
pp. 71-84
Author(s):  
D. Vivek ◽  
K. Kanagarajan ◽  
E. M. Elsayed
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Existence Of Solution ◽  
Ulam Stability ◽  
Hadamard Fractional Derivative ◽  
Stability Results

Abstract In this paper, we investigate the existence of solution of integro-differential equations (IDEs) with Hilfer-Hadamard fractional derivative. The main results are obtained by using Schaefer’s fixed point theorem. Some Ulam stability results are presented.

Sign in / Sign up

Export Citation Format

Share Document