Global asymptotic stability of solutions of a functional integral equation

DOI10.1016/j.na.2007.07.038zbMath1154.45005OpenAlexW1975212685MaRDI QIDQ944757

Bapurao C. Dhage, Józef Banaś

Publication date: 10 September 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.07.038

zbMATH Keywords

measure of noncompactnessglobal asymptotic stabilityfixed point theoremfunctional integral equation

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Asymptotics of solutions to integral equations (45M05) Stability theory for integral equations (45M10)

Related Items (39)

On the measure of noncompactness in $L_p(\mathbb{R}^+)$ and applications to a product of $n$-integral equations ⋮ Existence and attractivity results for nonlinear first-order random differential equations ⋮ Existence and attractivity of global solutions for a class of fractional quadratic integral equations in Banach space ⋮ Existence and stability results for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations ⋮ Measure of noncompactness on <img width=72 height=35 src="http:/fbpe/img/cubo/v17n1/art07-1.jpg">and applications ⋮ On global existence and attractivity results for nonlinear functional integral equations ⋮ Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces ⋮ Existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on \(L^p(\mathbb{R}_+)\) ⋮ Construction of a measure of noncompactness on \(BC(\Omega)\) and its application to Volterra integral equations ⋮ Existence and attractivity for the Darboux problem of fractional order neutral differential equations ⋮ Existence of solutions for a class of system of functional integral equation via measure of noncompactness ⋮ Solvability of functional integral equations in the Fréchet space \(C(\Omega)\) ⋮ Fractional order integral equations of two independent variables ⋮ Global existence and stability results for Hadamard--Volterra--Stieltjes integral equations ⋮ Nonlinear fractional order Riemman-Liouville Volterra-Stieltjes partial integral equations on unbounded domains ⋮ Coupled hybrid fixed point theory in a partially ordered metric space and attractivity of nonlinear hybrid fractional integral equations ⋮ Coupled hybrid fixed point theory involving the sum and product of three coupled operators in a partially ordered Banach algebra with applications ⋮ Existence and asymptotic stability of solutions of a functional integral equation via a consequence of Sadovskii's theorem ⋮ Family of mappings with an equicontractive-type condition ⋮ Solvability of nonlinear integral equations of Volterra type ⋮ Modified version of fixed point theorems and their applications on a fractional hybrid differential equation in the space of continuous tempered functions ⋮ Asymptotic behaviour of nonlinear quadratic functional integral equations involving Carathéodory ⋮ Global stability results for Volterra-Hadamard random partial fractional integral equations ⋮ Existence, stability and global attractivity results for nonlinear Riemann-Liouville fractional differential equations ⋮ Fixed point theorems in the Fréchet space \(\mathcal C(\mathbb R_+)\) and functional integral equations on an unbounded interval ⋮ Global attractivity for fractional order delay partial integro-differential equations ⋮ Existence and attractivity results for coupled systems of nonlinear Volterra-Stieltjes multidelay fractional partial integral equations ⋮ On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order ⋮ Existence and global attractivity of solutions of a nonlinear functional integral equation ⋮ The behaviour of measures of noncompactness in \(L^\infty (\mathbb {R}^n)\) with application to the solvability of functional integral equations ⋮ Existence and global attractivity of solutions of a nonlinear functional integral equation ⋮ Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions ⋮ Pseudo-almost periodic solutions of neutral integral and differential equations with applications ⋮ Uniform asymptotic stability of solutions of fractional functional differential equations ⋮ Local attractivity for integro-differential equations with noncompact semigroups ⋮ On local attractivity of solutions of a functional integral equation of fractional order with deviating arguments ⋮ Analysis of the Euler and trapezoidal discretization methods for the numerical solution of nonlinear functional Volterra integral equations of Urysohn type ⋮ Existence and Attractivity Theorems for Nonlinear Hybrid Fractional Integrodifferential Equations with Anticipation and Retardation ⋮ Fixed point theorems in WC-Banach algebras and their applications to infinite systems of integral equations

Cites Work

• Existence principles for nonlinear resonant operator and integral equations
• Fixed points and stability of an integral equation: nonuniqueness.
• An application of a measure of noncompactness in the study of asymptotic stability
• The global attractivity and asymptotic stability of solution of a nonlinear integral equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Global asymptotic stability of solutions of a functional integral equation