scholarly journals Existence of Tripled Fixed Points for a Class of Condensing Operators in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Vatan Karakaya ◽  
Nour El Houda Bouzara ◽  
Kadri Doğan ◽  
Yunus Atalan
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
General System ◽  
Nonlinear Integral Equations ◽  
Condensing Operators

We give some results concerning the existence of tripled fixed points for a class of condensing operators in Banach spaces. Further, as an application, we study the existence of solutions for a general system of nonlinear integral equations.

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 Common fixed points of biased maps of type(A)and applications

1998 ◽  
Vol 21 (4) ◽  
pp. 681-693 ◽  
Author(s):  
H. K. Pathak ◽  
Y. J. Cho ◽  
S. M. Kang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Type A ◽  
Common Fixed Points ◽  
Compatible Maps ◽  
Nonlinear Integral Equations

A generalization of compatible maps of type(A)called “biased maps of type(A)” is introduced and used to prove fixed point theorems for certain contractions of four maps. Extensions of known results are thereby obtained, i.e., the results of Pathak, Prasad, Jungck et al. are improved. Some problems on convergence of self-maps and fixed points are also discussed. Further, we use our main results to show the existence of solutions of nonlinear integral equations.

scholarly journals On New χ -Fixed Point Results for λ − Υ , χ -Contractions in Complete Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Babak Mohammadi ◽  
Wutiphol Sintunavarat ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Partial Metric ◽  
Nonlinear Integral Equations ◽  
Complete Metric Spaces ◽  
Partial Metric Spaces ◽  
Theoretical Results

The main aim of this work is to introduce the new concept of λ − Υ , χ -contraction self-mappings and prove the existence of χ -fixed points for such mappings in metric spaces. Our results generalize and improve some results in existing literature. Moreover, some fixed point results in partial metric spaces can be derived from our χ -fixed points results. Finally, the existence of solutions of nonlinear integral equations is investigated via the theoretical results in this work.

scholarly journals New classes of condensing operators and application to solvability of singular integral equations

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 843-860
Author(s):  
A. Aghajani ◽  
M. Aliaskari ◽  
D. O’Regan
Keyword(s):  
Banach Algebra ◽  
Fixed Points ◽  
Banach Spaces ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Condensing Operators ◽  
The Way

In this paper, we introduce the notion of Krasnoselskii and Dugundji-Granas condensing operators in Banach spaces. In order to pave the way for a study the solvability of some classes of singular integral equations in the Banach algebra C[a,b], we provide some results for the existence of fixed points for such condensing operators. An example is presented to show the applicability of the results.

Weak compactness of Fréchet-derivatives: application to composition operators

1980 ◽  
Vol 29 (4) ◽  
pp. 399-406
Author(s):  
Peter Dierolf ◽  
Jürgen Voigt
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Sobolev Spaces ◽  
Composition Operators ◽  
Weak Compactness ◽  
Nonlinear Integral Equations ◽  
Weakly Compact ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Compact Map

AbstractWe prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.

Simulation functions and Meir–Keeler condensing operators with application to integral equations

2021 ◽  
Author(s):  
Moosa Gabeleh ◽  
Mehdi Asadi ◽  
Pradip Ramesh Patle
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Darbo’S Fixed Point Theorem ◽  
Simulation Functions ◽  
Condensing Operators

We propose a new concept of condensing operators by using a notion of measure of non-compactness in the setting of Banach spaces and establish a new generalization of Darbo’s fixed point theorem. We also show the applicability of our results to integral equations. A concrete example will be presented to support the application part.

Existence of solutions of fuzzy integral equations in Banach spaces

1995 ◽  
Vol 72 (3) ◽  
pp. 373-378 ◽  
Author(s):  
Jong Yeoul Park ◽  
Young Chel Kwun ◽  
Jae Ug Jeong
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
Fuzzy Integral

scholarly journals Generalized contraction mappings of rational type and applications to nonlinear integral equations

2018 ◽  
Vol 38 (1) ◽  
pp. 131-149
Author(s):  
José R. Morales ◽  
Edixon M. Rojas ◽  
Ravindra K. Bisht
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Generalized Contraction ◽  
Nonlinear Integral Equations ◽  
Contraction Mappings ◽  
New Class ◽  
Common Fixed Point Theorems ◽  
Rational Type

The aim of the present paper is to introduce a new class of pair of contraction mappings, called ψ − (α, β, m)-contraction pairs, and obtain common fixed point theorems for a pair of mappings in this class, satisfying a minimal commutativity condition. Afterwards, we will use mappings in this class to analyze the existence of solutions for a class of nonlinear integral equations on the space of con- tinuous functions and in some of its subspaces. Concrete examples are also provided in order to illustrate the applicability of the results.

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