Random fixed point theorem in generalized Banach space and applications

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.

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Random Approximation with Weak Contraction Random Operator and Random Fixed Point Theorem for Nonexpansive Random Mapping

2010 First ACIS International Symposium on Cryptography, and Network Security, Data Mining and Knowledge Discovery, E-Commerce and Its Applications, and Embedded Systems ◽

10.1109/cdee.2010.89 ◽

2010 ◽

Author(s):

Suhong Li ◽

Lingmin Zhang ◽

Xin Xiao ◽

Lihua Li ◽

Hongwu Yin ◽

...

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Random Operator ◽

Weak Contraction ◽

Random Fixed Point ◽

Random Mapping ◽

Random Fixed Point Theorem

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Random fixed point theorems for asymptotic1-set contraction operators

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171202006105 ◽

2002 ◽

Vol 31 (7) ◽

pp. 407-412 ◽

Cited By ~ 1

Author(s):

P. Vijayaraju

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Fixed Point Theorems ◽

Random Fixed Point ◽

Random Fixed Point Theorem

Random fixed point theorems for condensing,1-set contraction selfless are known. But no random fixed point theorem for more general asymptotic1-set contraction selfmaps is yet available. The purpose of this paper is to prove random fixed point theorems for such maps.

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Random fixed point theorems for Ciric quasi contraction in cone random metric spaces

Annals of West University of Timisoara - Mathematics and Computer Science ◽

10.1515/awutm-2015-0009 ◽

2015 ◽

Vol 53 (1) ◽

pp. 163-175

Author(s):

G. S. Saluja

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Caristi’s random fixed point theorem for generalized distance on Polish spaces

Carpathian Journal of Mathematics ◽

10.37193/cjm.2016.03.04 ◽

2016 ◽

Vol 32 (3) ◽

pp. 285-292

Author(s):

AREERAT ARUNCHAI ◽

◽

SOMYOT PLUBTIENG ◽

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Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Fixed Point Theorems ◽

Random Fixed Point ◽

Caristi’S Fixed Point Theorem ◽

Polish Spaces ◽

Random Fixed Point Theorem ◽

Generalized Distance ◽

Caristi's Fixed Point Theorem

In this paper, we present the random version of generalized Caristi’s fixed point theorem for generalized distance on Polish spaces. Moreover, we prove some Caristi’s random fixed point theorems for multi-valued mappings on Polish spaces. Our results in this paper extend and improve some known results in the literature.

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Existence results for a class of random delay integrodifferential equations

Random Operators and Stochastic Equations ◽

10.1515/rose-2021-2054 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Amadou Diop ◽

Mamadou Abdul Diop ◽

K. Ezzinbi

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Operator Theory ◽

Mild Solutions ◽

Random Delay ◽

Random Fixed Point ◽

Unbounded Delay ◽

Carathéodory Conditions ◽

Random Fixed Point Theorem

Abstract In this paper, we consider a class of random partial integro-differential equations with unbounded delay. Existence of mild solutions are investigated by using a random fixed point theorem with a stochastic domain combined with Schauder’s fixed point theorem and Grimmer’s resolvent operator theory. The results are obtained under Carathéodory conditions. Finally, an example is provided to illustrate our results.

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