scholarly journals Existence results for Volterra-Stieltjes quadratic integral equations on an unbounded interval

2006 ◽  
Vol 98 (1) ◽  
pp. 143 ◽  
Author(s):  
Jósef Banas
Keyword(s):  
Existence Theorems ◽  
Existence Results ◽  
Stieltjes Integral ◽  
Measures Of Noncompactness ◽  
Unbounded Interval ◽  
Fixed Point Principle ◽  
Suitable Combination ◽  
Quadratic Integral ◽  
Schauder Fixed Point ◽  
Quadratic Integral Equations

We prove a few existence results for a nonlinear quadratic Volterra-Stieltjes integral equation on an unbounded interval. Our proof depends on suitable combination of the technique of measures of noncompactness and the Schauder fixed point principle. Such an approach permits us to obtain existence theorems under rather general assumptions.

scholarly journals Existence Theorems for Some Quadratic Integral Equations

1998 ◽  
Vol 222 (1) ◽  
pp. 276-285 ◽  
Author(s):  
Józef Banaś ◽  
Millenia Lecko ◽  
Wagdy Gomaa El-Sayed
Keyword(s):  
Integral Equations ◽  
Existence Theorems ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

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 A Unified Approach to Some Classes of Nonlinear Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Nurgali K. Ashirbayev ◽  
Józef Banaś ◽  
Raina Bekmoldayeva
Keyword(s):  
Integral Equations ◽  
Stieltjes Integral ◽  
View Point ◽  
Unified Approach ◽  
Nonlinear Integral Equations ◽  
Several Variables ◽  
Quadratic Integral ◽  
Function Of Two Variables ◽  
Fractional Orders ◽  
Quadratic Integral Equations

We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdélyi-Kober type. Those integral equations play very significant role in applications to the description of numerous real world events. Our aim is to show that the mentioned integral equations can be treated from the view point of nonlinear Volterra-Stieltjes integral equations. The Riemann-Stieltjes integral appearing in those integral equations is generated by a function of two variables. The choice of a suitable generating function enables us to obtain various kinds of integral equations. Some results concerning nonlinear Volterra-Stieltjes integral equations in several variables will be also discussed.

scholarly journals Existence Results for Block Matrix Operator of Fractional Orders in Banach Algebras

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 856 ◽  
Author(s):  
Hind Hashem ◽  
Ahmed El-Sayed ◽  
Dumitru Baleanu
Keyword(s):  
Existence Of Solutions ◽  
Banach Algebras ◽  
Coupled System ◽  
Existence Results ◽  
Direct Application ◽  
Block Matrix ◽  
Quadratic Integral ◽  
The Stability ◽  
Fractional Orders ◽  
Quadratic Integral Equations

This paper is concerned with proving the existence of solutions for a coupled system of quadratic integral equations of fractional order in Banach algebras. This result is a direct application of a fixed point theorem of Banach algebras. Some particular cases, examples and remarks are illustrated. Finally, the stability of solutions for that coupled system are studied.

Existence results for nonlinear quadratic integral equations of fractional order in Banach algebra

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Ahmed El-Sayed ◽  
Hind Hashem
Keyword(s):  
Integral Equation ◽  
Banach Algebra ◽  
Existence Theorem ◽  
Fractional Order ◽  
Continuous Solution ◽  
Functional Integral ◽  
Existence Results ◽  
Quadratic Functional ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

AbstractWe present an existence theorem for at least one continuous solution for a nonlinear quadratic functional integral equation of fractional order. Also, a general quadratic integral of fractional order will be considered.

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].

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 Theorems on Solvability of Constrained Inclusion Problems and Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Teffera M. Asfaw
Keyword(s):  
Reflexive Banach Space ◽  
Existence Theorems ◽  
Maximal Monotone ◽  
Existence Of Solution ◽  
Existence Results ◽  
Uniformly Convex ◽  
Homotopy Invariance ◽  
Inclusion Problems ◽  
Compact Resolvents ◽  
Nonlinear Variational Inequality

LetXbe a real locally uniformly convex reflexive Banach space with locally uniformly convex dual spaceX⁎. LetT:X⊇D(T)→2X⁎be a maximal monotone operator andC:X⊇D(C)→X⁎be bounded and continuous withD(T)⊆D(C). The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the typeT+Cprovided thatCis compact orTis of compact resolvents under weak boundary condition. The Nagumo degree mapping and homotopy invariance results are employed. The paper presents existence results under the weakest coercivity condition onT+C. The operatorCis neither required to be defined everywhere nor required to be pseudomonotone type. The results are applied to prove existence of solution for nonlinear variational inequality problems.

Sign in / Sign up

Export Citation Format

Share Document