scholarly journals Some random fixed point theorems with PPF dependence for weakly contractive random operator

2013 ◽  
pp. 489-499
Author(s):  
Pham The Anh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Random Operator ◽  
Random Fixed Point ◽  
Weakly Contractive

Random iterative algorithms and almost sure stability in Banach spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3611-3626 ◽  
Author(s):  
Abdul Khan ◽  
Vivek Kumar ◽  
Satish Narwal ◽  
Renu Chugh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Algorithms ◽  
Random Operator ◽  
Almost Sure Stability ◽  
Random Fixed Point ◽  
Stochastic Version ◽  
Contractive Type ◽  
Bochner Integrability ◽  
Weakly Contractive

Many popular iterative algorithms have been used to approximate fixed point of contractive type operators. We define the concept of generalized ?-weakly contractive random operator T on a separable Banach space and establish Bochner integrability of random fixed point and almost sure stability of T with respect to several random Kirk type algorithms. Examples are included to support new results and show their validity. Our work generalizes, improves and provides stochastic version of several earlier results by a number of researchers.

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.

Some Random Fixed Point Theorems and Comparing Random Operator Equations

2011 ◽  
Vol 52-54 ◽  
pp. 127-132
Author(s):  
Ning Chen ◽  
Bao Dan Tian ◽  
Ji Qian Chen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Random Operator ◽  
The Other ◽  
Operator Equations ◽  
Random Solution ◽  
Random Fixed Point ◽  
Other Hand ◽  
The Common

In this paper, some new results are given for the common random solution for a class of random operator equations which generalize several results in [4], [5] and [6] in Banach space. On the other hand, Altman’s inequality is also extending into the type of the determinant form. And comparing some solution for several examples, main results are theorem 2.3, theorem 3.3-3.4, theorem 4.1 and theorem 4.3.

Random fixed points of asymptotically nonexpansive random operators on unbounded domains

2008 ◽  
Vol 58 (6) ◽  
Author(s):  
Ismat Beg ◽  
Mujahid Abbas
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Unbounded Domains ◽  
Random Operator ◽  
Random Operators ◽  
Random Fixed Point ◽  
Random Fixed Points ◽  
Asymptotically Nonexpansive

AbstractThe aim of this paper is to prove some random fixed point theorems for asymptotically nonexpansive random operator defined on an unbounded closed and starshaped subset of a Banach space.

Random fixed point theorem in generalized Banach space and applications

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Moulay Larbi Sinacer ◽  
Juan Jose Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Random Operator ◽  
Existence Of Solution ◽  
Random Fixed Point ◽  
Random Differential Equations ◽  
Random Fixed Point Theorem

AbstractIn this paper, we prove some random fixed point theorems in generalized Banach spaces. We establish a random version of a Krasnoselskii-type fixed point theorem for the sum of a contraction random operator and a compact operator. The results are used to prove the existence of solution for random differential equations with initial and boundary conditions. Finally, some examples are given to illustrate the results.

scholarly journals Random fixed point theorems on product spaces

1993 ◽  
Vol 6 (2) ◽  
pp. 95-106 ◽  
Author(s):  
Ismat Beg ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Random Operator ◽  
Product Spaces ◽  
Random Fixed Point

The existence of random fixed point of a locally contractive random operator in first variable on product spaces is proved. The concept “continuous random height-selection” is discussed. Some random fixed point theorems for nonexpansive self and nonself maps are also obtained in product spaces.

scholarly journals Random fixed point theorems for multivalued nonexpansive non-self-random operators

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
S. Plubtieng ◽  
P. Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Compact Convex ◽  
Measurable Space ◽  
Contractive Mapping ◽  
Random Operator ◽  
Random Operators ◽  
Random Fixed Point ◽  
The Family ◽  
Separable Subset

Let (Ω,Σ) be a measurable space, with Σ a sigma-algebra of subset of Ω, and let C be a nonempty bounded closed convex separable subset of a Banach space X, whose characteristic of noncompact convexity is less than 1, KC(X) the family of all compact convex subsets of X. We prove that a multivalued nonexpansive non-self-random operator T:Ω×C→KC(X), 1-χ-contractive mapping, satisfying an inwardness condition has a random fixed point.

Fixed point theorems for generalized weakly contractive mappings

2011 ◽  
Vol 74 (6) ◽  
pp. 2116-2126 ◽  
Author(s):  
Binayak S. Choudhury ◽  
P. Konar ◽  
B.E. Rhoades ◽  
N. Metiya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Contractive Mappings ◽  
Weakly Contractive
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