scholarly journals α-Coupled Fixed Points and Their Application in Dynamic Programming

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
J. Harjani ◽  
J. Rocha ◽  
K. Sadarangani
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Coupled Fixed Point ◽  
Uniqueness Of Solutions ◽  
Bounded Functions ◽  
Definition Of ◽  
Coupled Fixed Points

We introduce the definition ofα-coupled fixed point in the space of the bounded functions on a setSand we present a result about the existence and uniqueness of such points. Moreover, as an application of our result, we study the problem of existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic programming.

New α-coupled fixed point theorem for 𝜃-contraction and its application to a class of systems of functional equations arising in dynamic programming

2018 ◽  
Vol 13 (03) ◽  
pp. 2050063
Author(s):  
P. Dhivya ◽  
M. Marudai
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Coupled Fixed Point ◽  
Uniqueness Of Solutions ◽  
Coupled Fixed Point Theorem ◽  
Bounded Functions

We introduce [Formula: see text]-coupled fixed point for [Formula: see text]-contractions in the space of bounded functions on a set [Formula: see text]. As an application of our result, we prove the existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic programming.

scholarly journals Coupled Fixed Point Theorems with New Implicit Relations and an Application

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
G. V. R. Babu ◽  
P. D. Sailaja
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Implicit Relation ◽  
Coupled Fixed Points

We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.

scholarly journals On a fixed point theorem and its application in dynamic programming

2015 ◽  
Vol 9 (2) ◽  
pp. 221-244 ◽  
Author(s):  
Ángel Almeida ◽  
Antonio-Francisco Roldán-López-de-Hierro ◽  
Kishin Sadarangani
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Uniqueness Of Solutions ◽  
Rational Type

In this paper, we present some fixed point theorems for contractions of rational type. These theorems generalize some other results appearing in the literature. Moreover, we present some examples illustrating our results. Finally, we present an application to the study of the existence and uniqueness of solutions to a class of functional equations arising in dynamic programming.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

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.

scholarly journals Common Fixed Point Theorems in Metric Spaces with Applications

2018 ◽  
Vol 11 (4) ◽  
pp. 1177-1190
Author(s):  
Pushpendra Semwal
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
System Of Functional Equations ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper we investigate the existence and uniqueness of common fixed point theorems for certain contractive type of mappings. As an application the existence and uniqueness of common solutions for a system of functional equations arising in dynamic programming are discuss by using the our results.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

scholarly journals 𝒥ℋ-Operator Pairs with Application to Functional Equations Arising in Dynamic Programming

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
A. Razani ◽  
B. Moeini
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Common Solution ◽  
The Common ◽  
Common Fixed Point Theorems

Some common fixed point theorems for𝒥ℋ-operator pairs are proved. As an application, the existence and uniqueness of the common solution for systems of functional equations arising in dynamic programming are discussed. Also, an example to validate all the conditions of the main result is presented.

scholarly journals Fixed point theorems for new contractions with application in dynamic programming

2021 ◽  
Vol 8 (2) ◽  
pp. 338-348
Author(s):  
Youssef Touail ◽  
◽  
Driss El Moutawakil ◽  
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Spaces ◽  
Uniqueness Of Solutions

In this study, we give a generalization of the well-known Reich fixed point in the setting of general topological spaces with τ -distances. As applications of the obtained result, we prove some fixed point theorems for new contraction types in metric spaces. Moreover, we establish the existence and the uniqueness of solutions for a class of functional equations arising in dynamic programming.

Fixed point theorems for a pair of single-valued operators in a metric space endowed with a reflexive relation

2017 ◽  
Vol 33 (3) ◽  
pp. 301-310
Author(s):  
MELANIA-IULIA DOBRICAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Uniqueness Theorems ◽  
Mixed Monotone Property ◽  
First Order ◽  
System Equation ◽  
Coupled Fixed Points

In this paper we provide some existence and uniqueness theorems for coupled fixed points for a pair of contractive operators satisfying a mixed monotone property, in a metric space endowed with a reflexive relation. An application to a first-order differential system equation with PBV conditions is also given to illustrate the utility of our results.

scholarly journals A Constructive Scheme for a Common Coupled Fixed Point Problems in Hilbert Space

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1717
Author(s):  
Kyung Soo Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Coupled Fixed Point ◽  
Common Coupled Fixed Point ◽  
Potential Applications ◽  
Fixed Point Iterations ◽  
Common Coupled Fixed Points ◽  
Coupled Fixed Points

Coupled fixed points have become the focus of interest in recent times, especially for their potential applications. Very recently, the idea of common coupled fixed point iterations has been introduced for approximating common coupled fixed points in linear spaces. Here, a coupled Mann pair iterative scheme is defined and is applied to the problem of finding common coupled fixed points of certain mappings. The discussion of the paper is in the context of Hilbert spaces.

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