scholarly journals On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Józef Banaś ◽  
Rafał Nalepa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Modulus Of Continuity ◽  
Existence Result ◽  
Sufficient Condition ◽  
Hölder Condition ◽  
Fredholm Type ◽  
Relative Compactness ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

We are going to study the space of real functions defined on a bounded metric space and having growths tempered by a modulus of continuity. We prove also a sufficient condition for the relative compactness in the mentioned function space. Using that condition and the classical Schauder fixed point theorem, we show the existence theorem for some quadratic integral equations of Fredholm type in the space of functions satisfying the Hölder condition. An example illustrating the mentioned existence result is also included.

scholarly journals Solvability of a Quadratic Integral Equation of Fredholm Type with Supremum in Hölder Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
J. Caballero Mena ◽  
R. Nalepa ◽  
K. Sadarangani
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Hölder Condition ◽  
Fredholm Type ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Holder Spaces

Using the classical Schauder fixed point theorem, we prove the existence of solutions of a quadratic integral equation of Fredholm type with supremum in the space of functions satisfying the Hölder condition.

Solvability of a 2 x 2 block operator matrix of chandrasekhar type on a Bananch algebra

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5169-5175 ◽  
Author(s):  
H.H.G. Hashem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Operator Matrix ◽  
Nonlinear Operators ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

scholarly journals Existence and stability of solutions for a system of quadratic integral equations in Banach algebras

2020 ◽  
Vol 19 (1) ◽  
pp. 203-218
Author(s):  
Said Baghdad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Banach Algebras ◽  
Main Tool ◽  
Stability Of Solutions ◽  
Existence And Stability ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

AbstractThe aim of this paper is to prove the existence and stability of solutions of a system of quadratic integral equations in the Banach algebra of continuous and bounded functions on unbounded rectangle. The main tool used in our considerations is the multiple fixed point theorem which is a consequence of Darbo’s fixed point theorem and the technique associated with measures of noncompactness. We also present an illustrative example.

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.

scholarly journals A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 256 ◽  
Author(s):  
Jarunee Soontharanon ◽  
Saowaluck Chasreechai ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Difference Equations ◽  
Existence Result ◽  
Coupled System ◽  
Half Line ◽  
Fractional Difference ◽  
Fractional Difference Equations

In this article, we propose a coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-line and study its existence result by using Schauder’s fixed point theorem. An example is provided to illustrate the results.

scholarly journals Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Shayma Adil Murad ◽  
Hussein Jebrail Zekri ◽  
Samir Hadid
Keyword(s):  
Banach Space ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Existence And Uniqueness Theorem ◽  
Integral Boundary ◽  
Fredholm Type ◽  
Type Integral

We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.

scholarly journals Solvability for generalized nonlinear two dimensional functional integral equations via measure of noncompactness

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Soniya Singh ◽  
Bhupander Singh ◽  
Kottakkaran Sooppy Nisar ◽  
Abd-Allah Hyder ◽  
M. Zakarya
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Two Dimensional ◽  
Functional Integral Equations

AbstractIn this article, we provide the existence result for functional integral equations by using Petryshyn’s fixed point theorem connecting the measure of noncompactness in a Banach space. The results enlarge the corresponding results of several authors. We present fascinating examples of equations.

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