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.

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 < ∞.

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.

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.

Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Fatima Bahidi ◽  
Bilel Krichen ◽  
Bilel Mefteh
Keyword(s):  
System Of Nonlinear Equations ◽  
Operator Matrix ◽  
Nonlinear Integral Equations ◽  
Nonlinear Operator Equations ◽  
Block Operator ◽  
Sequential Continuity ◽  
Block Operator Matrices ◽  
Measures Of Weak Noncompactness ◽  
Locally Convex Topology ◽  
Locally Convex

Abstract The purpose of this paper is to prove some fixed point results dealing with a system of nonlinear equations defined in an angelic Hausdorff locally convex space ( X , { | ⋅ | p } p ∈ Λ ) (X,\{\lvert\,{\cdot}\,\rvert_{p}\}_{p\in\Lambda}) having the 𝜏-Krein–Šmulian property, where 𝜏 is a weaker Hausdorff locally convex topology of 𝑋. The method applied in our study is connected with a family Φ Λ τ \Phi_{\Lambda}^{\tau} -MNC of measures of weak noncompactness and with the concept of 𝜏-sequential continuity. As a special case, we discuss the existence of solutions for a 2 × 2 2\times 2 block operator matrix with nonlinear inputs. Furthermore, we give an illustrative example for a system of nonlinear integral equations in the space C ⁢ ( R + ) × C ⁢ ( R + ) C(\mathbb{R}^{+})\times C(\mathbb{R}^{+}) to verify the effectiveness and applicability of our main result.

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 Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 130
Author(s):  
Mohamed Amine Farid ◽  
Karim Chaira ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Weak Topology ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Nonlinear Operator ◽  
Banach Algebras ◽  
Measure Of Weak Noncompactness

In this paper, we prove some fixed point theorems for the nonlinear operator A · B + C in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the application of our results to a nonlinear integral equation in Banach algebra.

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