The existence of asymptotically stable solutions for a nonlinear functional integral equation with values in a general Banach space

2011 ◽  
Vol 74 (18) ◽  
pp. 7111-7125
Author(s):  
Le Thi Phuong Ngoc ◽  
Nguyen Thanh Long
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Functional Integral ◽  
Asymptotically Stable ◽  
Nonlinear Functional ◽  
Stable Solutions ◽  
General Banach Space

scholarly journals Asymptotically Stable Solutions of a Generalized Fractional Quadratic Functional-Integral Equation of Erdélyi-Kober Type

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Abdalla Darwish ◽  
Beata Rzepka
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Stable Solution ◽  
Functional Integral ◽  
Quadratic Functional ◽  
Asymptotically Stable ◽  
Stable Solutions ◽  
Asymptotically Stable Solution

We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach spaceBC(ℝ+). We show that this equation has at least one asymptotically stable solution.

Asymptotic stability of solutions for a class of nonlinear functional integral equations of fractional order

2016 ◽  
Vol 53 (2) ◽  
pp. 256-288
Author(s):  
Ümit Çakan ◽  
İsmet Özdemir
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Asymptotically Stable ◽  
Stability Of Solutions ◽  
Nonlinear Functional ◽  
Bounded Functions ◽  
Stable Solutions ◽  
Functional Integral Equations

In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of asymptotically stable solutions of some nonlinear functional integral equations in the space of continuous and bounded functions on R+ = [0,∞). We also give some examples satisfying the conditions our existence theorem.

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