scholarly journals Some Algebraic and topological random fixed point theorems with applications to nonlinear random integral equations

2004 ◽  
Vol 35 (4) ◽  
pp. 321-346 ◽  
Author(s):  
B. C. Dhage
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Random Operators ◽  
Random Fixed Point ◽  
Nonlinear Functional ◽  
Monotonicity Conditions ◽  
Random Integral ◽  
Equation Of Mixed Type

In this paper some algebraic and topological random fixed point theorems are proved involving the three random operators on a Banach algebra and they are further applied to a certain nonlinear functional random integral equation of mixed type for proving the existence as well as existence of extremal random solutions under the generalized Lipschizicity, Carath´eodory and monotonicity conditions.

scholarly journals Random fixed point theorems in Banach algebras with applications to random integral equations

2003 ◽  
Vol 34 (1) ◽  
pp. 29-44
Author(s):  
B. C. Dhage
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Banach Algebras ◽  
Random Solution ◽  
Random Fixed Point ◽  
Nonlinear Functional ◽  
Carathéodory Conditions ◽  
Random Integral

The present paper studies the random versions of some deterministic fixed point theorems of Dhage [5] and Dhage and Regon [7]. Applications are given to a certain nonlinear functional random integral equation for proving the existence of random solution under the generalized Lipschitzicity and Caratheodory conditions.

scholarly journals Monotone iterative technique for Caratheodory theory of nonlinear functional random integral equations

2002 ◽  
Vol 33 (4) ◽  
pp. 341-352 ◽  
Author(s):  
B. C. Dhage
Keyword(s):  
Banach Space ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Random Fixed Point ◽  
Nonlinear Functional ◽  
Monotone Iterative ◽  
Monotonicity Conditions ◽  
Random Integral

In this paper some random fixed point theorems for the mappings on an ordered Banach space are proved. As applications, the existence of the extremal solutions of some nonlinear functional random integral equations is obtained under certain monotonicity conditions.

Random fixed point theorems for Caristi type random operators

2007 ◽  
Vol 25 (1-2) ◽  
pp. 425-434 ◽  
Author(s):  
Ismat Beg ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Random Operators ◽  
Random Fixed Point

scholarly journals Global Asymptotic Stability for Nonlinear Functional Integral Equation of Mixed Type

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zhinan Xia
Keyword(s):  
Integral Equation ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Mixed Type ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem ◽  
Equation Of Mixed Type ◽  
Stability Of The Solution

The existence results of global asymptotic stability of the solution are proved for functional integral equation of mixed type. The measure of noncompactness and the fixed-point theorem of Darbo are the main tools in carrying out our proof. Furthermore, some examples are given to show the efficiency and usefulness of the main findings.

scholarly journals Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces

1994 ◽  
Vol 7 (4) ◽  
pp. 569-580 ◽  
Author(s):  
Ismat Beg ◽  
Naseer Shahzad
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Random Operators ◽  
Random Coincidence ◽  
Random Fixed Point ◽  
Random Fixed Points ◽  
Multivalued Operators ◽  
Contractive Type

The existence of random fixed points. for nonexpansive and pseudocontractive random multivalued operators defined on unbounded subsets of a Banach space is proved. A random coincidence point theorem for a pair of compatible random multivalued operators is established.

scholarly journals Random Fixed Point Theorems of Random Comparable Operators and an Application

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Jiandong Yin ◽  
Zhongdong Liu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Monotone Operators ◽  
Hammerstein Integral Equation ◽  
Random Fixed Point ◽  
Partially Ordered ◽  
Ordered Banach Spaces

We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. Finally, as an application, we consider the existence of the solution of a random Hammerstein integral equation.

scholarly journals Some Random Fixed-Point Theorems for Weakly Contractive Random Operators in a Separable Banach Space

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Kenza Benkirane ◽  
Abderrahim EL Adraoui ◽  
El Miloudi Marhrani
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Fixed Point Theorems ◽  
Stochastic Integral ◽  
Equation System ◽  
Random Operators ◽  
Stochastic Integral Equation ◽  
Random Fixed Point ◽  
Weakly Contractive ◽  
Uniqueness Of A Solution

The aim of this paper is to prove a common random fixed-point and some random fixed-point theorems for random weakly contractive operators in separable Banach spaces. A random Mann iterative process is introduced to approximate the fixed point. Finally, the main result is supported by an example and used to prove the existence and the uniqueness of a solution of a nonlinear stochastic integral equation system.

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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