scholarly journals On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock–Kurzweil integrals

2004 ◽  
Vol 83 (3) ◽  
pp. 257-267 ◽  
Author(s):  
Aneta Sikorska-Nowak
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
Nonlinear Integral Equations

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.

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.

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.

scholarly journals SOME COMMON FIXED POINT RESULTS FOR RATIONAL CONTRACTION TYPE VIA THE C-CLASS FUNCTIONS ON METRIC SPACES

2019 ◽  
pp. 231
Author(s):  
Nguyen Thi Thanh Ly ◽  
Nguyen Trung Hieu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Nonlinear Integral Equations ◽  
Contraction Type ◽  
Rational Contraction

The purpose of this paper is to prove some common fixed point results for rational contraction type via the C-class functions on metric spaces. As an application, we study the existence of solutions to the system of nonlinear integral equations.

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.

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