scholarly journals Existence Theorem for Integral and Functional Integral Equations with Discontinuous Kernels

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ezzat R. Hassan
Keyword(s):  
Existence Theorem ◽  
Integral Equations ◽  
Functional Integral ◽  
Volterra Integral Equations ◽  
Extremal Solutions ◽  
Volterra Type ◽  
Discontinuous Kernels ◽  
Functional Integral Equations

Existence of extremal solutions of nonlinear discontinuous integral equations of Volterra type is proved. This result is extended herein to functional Volterra integral equations (FVIEs) and to a system of discontinuous VIEs as well.

scholarly journals Comment on “Existence Theorem for Integral and Functional Integral Equations with Discontinuous Kernels”

2015 ◽  
Vol 2015 ◽  
pp. 1-3
Author(s):  
Krzysztof A. Topolski
Keyword(s):  
Existence Theorem ◽  
Integral Equations ◽  
Functional Integral ◽  
Discontinuous Kernels ◽  
Functional Integral Equations

We present a counterexample to the main result of the abovementioned paper showing that this result is false and cannot be improved in a simple way.

scholarly journals A Cone Measure of Noncompactness and Some Generalizations of Darbo’s Theorem with Applications to Functional Integral Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Mohamed Jleli ◽  
Mohammad Mursaleen ◽  
Kishin Sadarangani ◽  
Bessem Samet
Keyword(s):  
Existence Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
System Of Integral Equations ◽  
Functional Integral Equations ◽  
Cone Measure

We introduce the concept of cone measure of noncompactness and obtain some generalizations of Darbo’s theorem via this new concept. As an application, we establish an existence theorem for a system of integral equations. An example is also provided to illustrate the obtained result.

scholarly journals Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces

2018 ◽  
Vol 51 (1) ◽  
pp. 131-140
Author(s):  
Saïd Abbas ◽  
Ravi P. Agarwal ◽  
Mouffak Benchohra ◽  
Farida Berhoun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Integral ◽  
Global Attractivity ◽  
Functional Integral ◽  
Fréchet Spaces ◽  
Volterra Type ◽  
Functional Integral Equations ◽  
Hadamard Fractional Integral

Abstract In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Hadamard fractional order. We use an extension of the Burton-Kirk fixed point theorem in Fréchet spaces.

Fuzzy Bezier splines with application to fuzzy functional integral equations

2020 ◽  
Vol 24 (8) ◽  
pp. 6069-6084
Author(s):  
Alexandru Mihai Bica ◽  
Constantin Popescu
Keyword(s):  
Integral Equations ◽  
Functional Integral ◽  
Functional Integral Equations
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