Solvability for generalized nonlinear functional integral equations in Banach spaces with applications

2021 ◽  
Vol 33 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Functional Integral Equations

scholarly journals The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Józef Banaś ◽  
Szymon Dudek
Keyword(s):  
Banach Algebra ◽  
Integral Equations ◽  
Banach Algebras ◽  
Functional Integral ◽  
Existence Results ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Half Axis ◽  
Functional Integral Equations

We study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally, that technique allows us to obtain some characterization of considered integral equations. An example illustrating the obtained results is also included.

scholarly journals On existence of extremal solutions of nonlinear functional integral equations in Banach algebras

2004 ◽  
Vol 2004 (3) ◽  
pp. 271-282 ◽  
Author(s):  
B. C. Dhage
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Banach Algebras ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Simple Method ◽  
Nonlinear Functional ◽  
Equations Of Mixed Type ◽  
Special Cases ◽  
Functional Integral Equations

An algebraic fixed point theorem involving the three operators in a Banach algebra is proved using the properties of cones and they are further applied to a certain nonlinear integral equations of mixed type x(t)=k(t,x(μ(t)))+[f(t,x(θ(t)))](q(t)+∫0σ(t)v(t,s)g(s,x(η(s)))ds) for proving the existence of maximal and minimal solutions. Our results include the earlier fixed point theorems of Dhage (1992 and 1999) as special cases with a different but simple method.

scholarly journals Solvability of functional-integral equations (fractional order) using measure of noncompactness

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Reza Arab ◽  
Hemant Kumar Nashine ◽  
N. H. Can ◽  
Tran Thanh Binh
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Arbitrary Measure ◽  
Functional Integral Equations

AbstractWe investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.

scholarly journals Further results on the existence of solutions for generalized fractional quadratic functional integral equations

2020 ◽  
Vol 1 (1) ◽  
pp. 33-46
Author(s):  
Mohammed S. Abdo
Keyword(s):  
Integral Equations ◽  
Existence Of Solutions ◽  
Continuous Solution ◽  
Functional Integral ◽  
Existence Results ◽  
Quadratic Functional ◽  
Nonlinear Functional Analysis ◽  
Nonlinear Functional ◽  
Special Cases ◽  
Functional Integral Equations

This paper discusses some existence results for at least one continuous solution for generalized fractional quadratic functional integral equations. Some results on nonlinear functional analysis including Schauder fixed point theorem are applied to establish the existence result for proposed equations. We improve and extend the literature by incorporated some well-known and commonly cited results as special cases in this topic. Further, we prove the existence of maximal and minimal solutions for these equations.

scholarly journals Partially condensing mappings in partially ordered normed linar spaces and applications to functional integral equations

2014 ◽  
Vol 45 (4) ◽  
pp. 397-426 ◽  
Author(s):  
Bapurao Chandrabahan Dhage
Keyword(s):  
Integral Equations ◽  
Fixed Point Theorems ◽  
Normed Linear Space ◽  
Global Attractivity ◽  
Nonlinear Problems ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Partially Ordered ◽  
Monotonicity Conditions ◽  
Functional Integral Equations

In this paper, the author introduces a notion of partially condensing mappings in a partially ordered normed linear space and proves some hybrid fixed point theorems under certain mixed conditions of algebra, analysis and topology. The applications of abstract results presented here are given to some nonlinear functional integral equations for proving the existence as well as global attractivity of the comparable solutions under certain monotonicity conditions. The abstract theory presented here is very much useful to develop the algorithms for the solutions of some nonlinear problems of analysis and allied areas of mathematics. A realization of of our hypotheses is also indicated by a numerical example.

scholarly journals On existence theorems for some generalized nonlinear functional-integral equations with applications

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2081-2091 ◽  
Author(s):  
Mishra Narayan ◽  
Mausumi Sen ◽  
Ram Mohapatra
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Functional Integral ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Functional Integral Equations

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

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