Convergence of successive approximations to a stochastic fixed point

1980 ◽  
Vol 17 (01) ◽  
pp. 297-299 ◽  
Author(s):  
Arun P. Sanghvi

This paper describes some sufficient conditions that ensure the convergence of successive random applications of a family of mappings {Γ α : α ∈ A} on a compact metric space (X, d) to a stochastic fixed point. The results are similar in spirit to a recent result of Yahav (1975).

1980 ◽  
Vol 17 (1) ◽  
pp. 297-299
Author(s):  
Arun P. Sanghvi

This paper describes some sufficient conditions that ensure the convergence of successive random applications of a family of mappings {Γα : α ∈ A} on a compact metric space (X, d) to a stochastic fixed point. The results are similar in spirit to a recent result of Yahav (1975).


Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.


2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Zhenhua Ma ◽  
Muhammad Nazam ◽  
Sami Ullah Khan ◽  
Xiangling Li

We study the sufficient conditions for the existence of a unique common fixed point of generalized αs-ψ-Geraghty contractions in an αs-complete partial b-metric space. We give an example in support of our findings. Our work generalizes many existing results in the literature. As an application of our findings we demonstrate the existence of the solution of the system of elliptic boundary value problems.


2012 ◽  
Vol 204-208 ◽  
pp. 4776-4779
Author(s):  
Lin Huang ◽  
Huo Yun Wang ◽  
Hong Ying Wu

By a dynamical system we mean a compact metric space together with a continuous map . This article is devoted to study of invariant scrambled sets. A dynamical system is a periodically adsorbing system if there exists a fixed point and a periodic point such that and are dense in . We show that every topological weakly mixing and periodically adsorbing system contains an invariant and dense Mycielski scrambled set for some , where has no isolated points. A subset is a Myceilski set if it is a countable union of Cantor sets.


2021 ◽  
Vol 52 ◽  
Author(s):  
Kushal Roy ◽  
Mantu Saha ◽  
Ismat Beg

We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on an S^{JS}- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results.


2021 ◽  
Vol 6 (12) ◽  
pp. 13092-13118
Author(s):  
Rizwan Rizwan ◽  
◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
Akbar Zada ◽  
...  

<abstract><p>In this paper, we consider switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness and generalized Ulam-Hyers-Rassias stability of our proposed model, with the help of generalized Diaz-Margolis's fixed point approach, over generalized complete metric space. We give an example which supports our main result.</p></abstract>


2015 ◽  
Vol 63 (1) ◽  
pp. 183-203 ◽  
Author(s):  
Janusz Migda

Abstract We introduce a topology, which we call the regional topology, on the space of all real functions on a given locally compact metric space. Next we obtain new versions of Schauder’s fixed point theorem and Ascoli’s theorem. We use these theorems and the properties of the iterated remainder operator to establish conditions under which there exist solutions, with prescribed asymptotic behaviour, of some difference and differential equations.


2009 ◽  
Vol 42 (4) ◽  
Author(s):  
D. O’Regan ◽  
M. Abbas

AbstractThe aim of this paper is to provide a necessary and sufficient condition for the existence of a common fixed point of three maps


1994 ◽  
Vol 17 (4) ◽  
pp. 713-716 ◽  
Author(s):  
Troy L. Hicks ◽  
Linda Marie Saliga

Supposef:C→XwhereCis a closed subset ofX. Necessary and sufficient conditions are given forfto have a fixed point. All results hold whenXis complete metric space. Several results hold in a much more general setting.


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