scholarly journals The solvability of a class of system of nonlinear integral equations via measure of noncompactness

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5969-5991 ◽  
Author(s):  
Habibollah Nasiri ◽  
Jamal Roshan
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
General System ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Nonlinear Functional ◽  
Functional Integral Equations ◽  
Class Of Functions

We propose a new notion of contraction mappings for two class of functions involving measure of noncompactness in Banach space. In this regard we present some theory and results on the existence of tripled fixed points and some basic Darbo?s type fixed points for a class of operators in Banach spaces. Also as an application we discuss the existence of solutions for a general system of nonlinear functional integral equations which satisfy in new certain conditions. Further we give an example to verify the effectiveness and applicability of our results.

scholarly journals On the solvability of some nonlinear functional integral equations on Lp(R+)

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1841-1850
Author(s):  
Mahmoud Bousselsal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Basic Tool ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem ◽  
Functional Integral Equations

In this paper, we prove theorems on the existence of solutions in Lp(R+), 1 ? p < ?, for some functional integral equations. The basic tool used in the proof is the fixed point theorem due to Darbo with respect to so called measure of noncompactness. The obtained results generalize and extend several ones obtained earlier in many papers and monographs. An example which shows the applicability of our results is also included.

The solvability of some nonlinear functional integral equations

2016 ◽  
Vol 53 (1) ◽  
pp. 7-21
Author(s):  
İsmet Özdemir ◽  
Ümit Çakan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Continuous Functions ◽  
Functional Integral ◽  
Space Of Continuous Functions ◽  
Nonlinear Functional ◽  
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 solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. We give also some examples which show that the obtained results are applicable

Existence of Solutions of Infinite Systems of Nonlinear Functional Integral Equations of N-Variables in C(I × I ×⋯ × I,m(ϕ))

2020 ◽  
pp. 2150147
Author(s):  
Hojjatollah Amiri Kayvanloo ◽  
Reza Allahyari
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Functional Integral ◽  
Hausdorff Measure Of Noncompactness ◽  
Nonlinear Functional ◽  
Infinite Systems ◽  
Condensing Operators ◽  
Functional Integral Equations

The aim of this paper is to investigate the solvability of infinite systems of nonlinear functional integral equations of [Formula: see text]-variables in [Formula: see text] by using the Hausdorff measure of noncompactness with the help of Meir–Keeler condensing operators. We also provide an illustrative example in support of our existence theorems.

Existence of tripled fixed points and solution of functional integral equations through a measure of noncompactness

2019 ◽  
Vol 35 (2) ◽  
pp. 193-208
Author(s):  
HABIB UR REHMAN ◽  
POOM KUMAM ◽  
SOMPONG DHOMPONGSA ◽  
◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
General System ◽  
Functional Integral ◽  
Tripled Fixed Point ◽  
General Class Of Functions ◽  
Functional Integral Equations ◽  
Class Of Functions

In this paper, we propose fixed point results through the notion of a measure of noncompactness and give a generalization of a Darbo’s fixed point theorem. We also prove some new tripled fixed point results via a measure of noncompactness for a more general class of functions. Our results generalize and extend some comparable results in the literature. Further, we apply the obtained fixed point theorems to prove the existence of solutions for a general system of non-linear functional integral equations. In the end, an example is given to illustrate the validity of our results.

scholarly journals The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2130
Author(s):  
Hasanen A. Hammad ◽  
Amal A. Khalil
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Integral Equations ◽  
Linear Functional ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
General Class Of Functions ◽  
Functional Integral Equations ◽  
Class Of Functions

Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of Darbo’s fixed point theorem is given in this manuscript. Furthermore, some novel quadruple fixed points results via a measure of noncompactness for a general class of functions are presented. Ultimately, the solutions to a system of non-linear functional integral equations by the fixed point results obtained are discussed, and non-trivial examples to illustrate the validity of our study are derived.

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.

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