On existence of solution of a class of quadratic-integral equations using contraction defined by simulation functions and measure of noncompactness

2018 ◽  
Vol 34 (3) ◽  
pp. 371-378
Author(s):  
M. MURSALEEN ◽  
◽  
REZA ARAB ◽  
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Applied Mathematics ◽  
Continuous Functions ◽  
Existence Of Solution ◽  
Measures Of Noncompactness ◽  
Darbo Fixed Point Theorem ◽  
Simulation Functions ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper we have introduced a new type of contraction condition using a class of simulation functions, in the sequel using the new contraction definition, involving measure of noncompactness; we establish few results on existence of fixed points of continuous functions defined on a subset of Banach space. This result also generalizes other related results obtained in Arab [Arab, R., Some generalizations of Darbo fixed point theorem and its application, Miskolc Math. Notes, 18 (2017), No. 2, 595–610], Banas [Bana ´ s, J. and Goebel, K., ´ Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, Dekker, New York, 60 (1980)]. The obtained results are used in establishing existence theorems for a class of nonlinear quadratic equation (which generalizes several types of fractional-quadratic integral equations such as Abel’s integral equation) defined on a closed and bounded subset of R. The existence of solution is established with the aid of a measure of noncompactness defined on function space C(I) introduced in [Banas, J. and Olszowy, L., ´ Measures of Noncompactness related to monotonicity, Comment. Math., 41 (2001), 13–23].

scholarly journals On perturbed quadratic integral equations and initial value problem with nonlocal conditions in Orlicz spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 86-94
Author(s):  
Mohamed M. A. Metwali
Keyword(s):  
Integral Equations ◽  
Initial Value Problem ◽  
Measure Of Noncompactness ◽  
Orlicz Spaces ◽  
Nonlocal Conditions ◽  
Initial Value ◽  
Hammerstein Integral Equations ◽  
Fixed Point Principle ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

AbstractThe existence of a.e. monotonic solutions for functional quadratic Hammerstein integral equations with the perturbation term is discussed in Orlicz spaces. We utilize the strategy of measure of noncompactness related to the Darbo fixed point principle. As an application, we discuss the presence of solution of the initial value problem with nonlocal conditions.

scholarly journals On some parameters in the space of regulated functions and their applications

2018 ◽  
Vol 34 (1) ◽  
pp. 17-30
Author(s):  
KINGA CICHON ◽  
◽  
MIECZYSŁAW CICHON ◽  
MOHAMED M. A. METWALI ◽  
◽  
...  
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Discontinuous Solutions ◽  
Discontinuous Functions ◽  
New Concepts ◽  
Quadratic Integral ◽  
Regulated Functions ◽  
Quadratic Integral Equations ◽  
Differential And Integral Equations

In this paper, we study a class of discontinuous functions being a space of solutions for some differential and integral equations. We investigate functions having finite one-sided limits, i.e. regulated functions. In the space of such functions, we introduce some new concepts like a modulus of equi-regularity or a measure of noncompactness, allowing us to unify the proofs for the results about existence for both continuous and discontinuous solutions. An example of applications for quadratic integral equations, essentially improving earlier ones, completes the paper.

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

scholarly journals Derivation of relativistic Yakubovsky equations under Poincaré invariance

2020 ◽  
Author(s):  
Kamada Hiroyuki
Keyword(s):  
Integral Equations ◽  
Momentum Space ◽  
Iteration Method ◽  
Body Force ◽  
Space Representation ◽  
Nucleon Scattering ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

Relativistic Faddeev-Yakubovsky four-nucleon scattering equations are derived including a 3-body force. We present these equations in the momentum space representation. The quadratic integral equations using the iteration method, in order to obtain boosted potentials and 3-body force, are demonstrated.

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.

Sign in / Sign up

Export Citation Format

Share Document