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 of solutions for a system of Chandrasekhar’s equations in Banach algebras underweak topology

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5949-5957
Author(s):  
Amor Fahem ◽  
Aref Jeribi ◽  
Najib Kaddachi
Keyword(s):  
Banach Algebra ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Coupled System ◽  
Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Continuous Operators ◽  
Quadratic Integral Equations

This paper is devoted to the study of a coupled system within fractional integral equations in suitable Banach algebra. In particular, we are concerned with a quadratic integral equations of Chandrasekhar type. The existence of solutions will be proved by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty, closed and convex subset of Banach algebra where the entries are weakly sequentially continuous 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.

scholarly journals Existence of solutions for hybrid fractional pantograph equations

2015 ◽  
Vol 9 (1) ◽  
pp. 150-167 ◽  
Author(s):  
Mohamed Darwish ◽  
Kishin Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Type Condition ◽  
Measures Of Noncompactness ◽  
Pantograph Equation ◽  
Liouville Fractional Derivative

In this paper, we study the existence of the hybrid fractional pantograph equation {D?0+[x(t)/f(t,x(t),x(?t))= g(t,x(t), x(?t)), 0 < t < 1, x(0) = 0, where ?,?,? ?((0,1) and D?0+ denotes the Riemann-Liouville fractional derivative. The results are obtained using the technique of measures of noncompactness in the Banach algebras and a fixed point theorem for the product of two operators verifying a Darbo type condition. Some examples are provided to illustrate our results.

Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg’s model type

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Afif Amar ◽  
Aref Jeribi ◽  
Bilel Krichen
Keyword(s):  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Operator Matrix ◽  
Model Type ◽  
Block Operator Matrix ◽  
Growing Cell ◽  
Block Operator ◽  
Abstract Boundary

AbstractIn this manuscript, we introduce and study the existence of solutions for a coupled system of differential equations under abstract boundary conditions of Rotenberg’s model type, this last arises in growing cell populations. The entries of block operator matrix associated to this system are nonlinear and act on the Banach space X p:= L p([0, 1] × [a, b]; dµ dv), where 0 ≤ a < b < ∞; 1 < p < ∞.

scholarly journals Implicit Hybrid Fractional Boundary Value Problem via Generalized Hilfer Derivative

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1937
Author(s):  
Abdellatif ‬Boutiara ◽  
Mohammed S. ‬Abdo ◽  
Mohammed A. ‬Almalahi ◽  
Hijaz Ahmad ◽  
Amira Ishan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Banach Algebras ◽  
Fractional Operators ◽  
Fractional Boundary Value Problem ◽  
Fractional Differential

This research paper is dedicated to the study of a class of boundary value problems for a nonlinear, implicit, hybrid, fractional, differential equation, supplemented with boundary conditions involving general fractional derivatives, known as the ϑ-Hilfer and ϑ-Riemann–Liouville fractional operators. The existence of solutions to the mentioned problem is obtained by some auxiliary conditions and applied Dhage’s fixed point theorem on Banach algebras. The considered problem covers some symmetry cases, with respect to a ϑ function. Moreover, we present a pertinent example to corroborate the reported results.

scholarly journals The p-Drazin inverse for operator matrix over Banach algebras

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4597-4605
Author(s):  
Huanyin Chen ◽  
Honglin Zou ◽  
Tugce Calci ◽  
Handan Kose
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Block Operator Matrix ◽  
Block Operator

An element a in a Banach algebra A has p-Drazin inverse provided that there exists b ? comm(a) such that b = b2a,ak-ak+1b?J(A) for some k ? N. In this paper, we present new conditions for a block operator matrix to have p-Drazin inverse. As applications, we prove the p-Drazin invertibility of the block operator matrix under certain spectral conditions.

scholarly journals Generalized form of fixed point theorems in Banach algebras under weak topology with an application

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4281-4296
Author(s):  
Najib Kaddachi
Keyword(s):  
Fixed Point ◽  
Weak Topology ◽  
Fixed Point Theorems ◽  
Banach Algebras ◽  
Coupled System ◽  
Operator Matrix ◽  
Multivalued Maps ◽  
Nonlinear Integral Equations ◽  
Block Operator ◽  
Measures Of Weak Noncompactness

In this manuscript, by means of the technique of measures of weak noncompactness, we establish a generalized form of fixed point theorems for a 2 x 2 block operator matrix involving multivalued maps acting on suitable Banach algebras. The results obtained are then applied to a coupled system of nonlinear integral equations.

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.

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