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 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.

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 Fixed point theorems in partial metric spaces with an application

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 617-624
Author(s):  
H.P. Masiha ◽  
F. Sabetghadam ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Fractional Boundary Value Problem ◽  
Partial Metric Spaces ◽  
Contractive Type ◽  
Ordered Partial Metric Space ◽  
Weakly Contractive

Matthews [12] introduced a new distance P on a nonempty set X, which he called a partial metric. The purpose of this paper is to present some fixed point results for weakly contractive type mappings in ordered partial metric space. An application to nonlinear fractional boundary value problem is also presented.

scholarly journals Seminormal Structure and Fixed Points of Cyclic Relatively Nonexpansive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Moosa Gabeleh ◽  
Naseer Shahzad
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Sufficient Conditions ◽  
Weakly Compact ◽  
Relatively Nonexpansive Mapping ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive ◽  
Contractive Type

LetAandBbe two nonempty subsets of a Banach spaceX. A mappingT:A∪B→A∪Bis said to be cyclic relatively nonexpansive ifT(A)⊆BandT(B)⊆AandTx-Ty≤x-yfor all (x,y)∈A×B. In this paper, we introduce a geometric notion of seminormal structure on a nonempty, bounded, closed, and convex pair of subsets of a Banach spaceX. It is shown that if (A,B) is a nonempty, weakly compact, and convex pair and (A,B) has seminormal structure, then a cyclic relatively nonexpansive mappingT:A∪B→A∪Bhas a fixed point. We also discuss stability of fixed points by using the geometric notion of seminormal structure. In the last section, we discuss sufficient conditions which ensure the existence of best proximity points for cyclic contractive type mappings.Erratum to “Seminormal Structure and Fixed Points of Cyclic Relatively Nonexpansive Mappings”

VISCOSITY APPROXIMATION METHODS OF RANDOM FIXED POINT SOLUTIONS AND RANDOM VARIATIONAL INEQUALITIES IN HILBERT SPACES

2011 ◽  
Vol 04 (02) ◽  
pp. 283-293 ◽  
Author(s):  
Poom Kumam ◽  
Somyot Plubtieng
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Random Operators ◽  
Random Fixed Point ◽  
Stochastic Version ◽  
Iterative Processes ◽  
Random Fixed Points ◽  
Inequality Theory ◽  
Viscosity Approximation Methods ◽  
Random Variational Inequalities

In this paper, we construct random iterative processes for nonexpansive random operators and study necessary conditions for these processes. It is shown that these random iterative processes converge to random fixed points of nonexpansive random operators and solve some random variational inequalities. We also proved that an implicit random iterative process converges to the random fixed point and solves these random variational inequalities. Our results can be viewed as a refinement and improvement of the previously known results for variational inequality theory and also give generalization stochastic version of some results of Xu [23].

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