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 Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mohamed Amine Farid ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
System Of Nonlinear Equations ◽  
Operator Matrix ◽  
Measure Of Weak Noncompactness ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Sequential Continuity ◽  
Schauder Fixed Point

In this paper, we establish some new variants of Leray–Schauder-type fixed point theorems for a 2 × 2 block operator matrix defined on nonempty, closed, and convex subsets Ω of Banach spaces. Note here that Ω need not be bounded. These results are formulated in terms of weak sequential continuity and the technique of De Blasi measure of weak noncompactness on countably subsets. We will also prove the existence of solutions for a coupled system of nonlinear equations with an example.

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 A Coupled System of Nonlinear Fractional Differential Equations with Multipoint Fractional Boundary Conditions on an Unbounded Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Guotao Wang ◽  
Bashir Ahmad ◽  
Lihong Zhang
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Unbounded Domain ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Fractional Boundary Conditions

This paper investigates the existence of solutions for a coupled system of nonlinear fractional differential equations withm-point fractional boundary conditions on an unbounded domain. Some standard fixed point theorems are applied to obtain the main results. The paper concludes with two illustrative examples.

New fixed point theorems for countably condensing maps with an application to functional integral inclusions

2021 ◽  
Vol 71 (6) ◽  
pp. 1487-1510
Author(s):  
Khaled Ben Amara ◽  
Aref Jeribi ◽  
Najib Kaddachi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Coupled System ◽  
Functional Integral ◽  
Operator Matrix ◽  
Block Operator ◽  
Functional Differential ◽  
Functional Differential Inclusions ◽  
Condensing Maps

Abstract This paper presents new fixed point theorems for 2 × 2 block operator matrix with countably condensing or countably 𝓓-set-contraction multi-valued inputs. Our theory will then be used to establish some new existence theorems for coupled system of functional differential inclusions in general Banach spaces under weak topology. Our results generalize, improve and complement a number of earlier works.

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 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 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.

A Study of Coupled Systems of ψ-Hilfer Type Sequential Fractional Differential Equations with Integro-Multipoint Boundary Conditions

2021 ◽  
Vol 5 (4) ◽  
pp. 162
Author(s):  
Ayub Samadi ◽  
Cholticha Nuchpong ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

In this paper, the existence and uniqueness of solutions for a coupled system of ψ-Hilfer type sequential fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions is investigated. The presented results are obtained via the classical Banach and Krasnosel’skiĭ’s fixed point theorems and the Leray–Schauder alternative. Examples are included to illustrate the effectiveness of the obtained results.

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