scholarly journals ASYMPTOTIC STABILITY OF FUNCTIONAL EQUATIONS BY FIXED POINT THEOREMS

2018 ◽  
Vol 22 (4) ◽  
Author(s):  
MUHAMMAD N. ISLAM ◽  
JEFFREY T. NEUGEBAUER
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Stability Of Functional Equations

scholarly journals Fixed Point Theory and the Ulam Stability

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Janusz Brzdęk ◽  
Liviu Cădariu ◽  
Krzysztof Ciepliński
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Stability Of Functional Equations ◽  
Banach’S Fixed Point Theorem ◽  
The Stability ◽  
First Time ◽  
Stability Results

The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940.

scholarly journals Asymptotic Stability of Nonlinear Discrete Fractional Pantograph Equations with Non-Local Initial Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 473
Author(s):  
Jehad Alzabut ◽  
A. George Maria Selvam ◽  
Rami Ahmad El-Nabulsi ◽  
D. Vignesh ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorems ◽  
Initial Conditions ◽  
Current Collector ◽  
Stability Of Solutions ◽  
Electric Bus ◽  
Pantograph Equation ◽  
Non Local

Pantograph, the technological successor of trolley poles, is an overhead current collector of electric bus, electric trains, and trams. In this work, we consider the discrete fractional pantograph equation of the form Δ*β[k](t)=wt+β,k(t+β),k(λ(t+β)), with condition k(0)=p[k] for t∈N1−β, 0<β≤1, λ∈(0,1) and investigate the properties of asymptotic stability of solutions. We will prove the main results by the aid of Krasnoselskii’s and generalized Banach fixed point theorems. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

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 On the probabilistic stability of some functional equations

2013 ◽  
Vol 29 (1) ◽  
pp. 125-132
Author(s):  
CLAUDIA ZAHARIA ◽  
◽  
DOREL MIHET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Of Functional Equations ◽  
The Stability ◽  
Stability Results

We establish stability results concerning the additive and quadratic functional equations in complete Menger ϕ-normed spaces by using fixed point theory. As particular cases, some theorems regarding the stability of functional equations in β - normed and quasi-normed spaces are obtained.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

scholarly journals Fixed point theorems for compatible mappings with applications to the solutions of functional equations arising in dynamic programmings

1997 ◽  
Vol 20 (4) ◽  
pp. 673-680 ◽  
Author(s):  
Nan-Jing Huang ◽  
Byung Soo Lee ◽  
Mee Kwang Kang
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Compatible Mappings ◽  
Common Fixed Point Theorems

Some common fixed point theorems for compatible mappings are shown As an application, the existence and uniqueness of common solutions for a class of functional equations arising in dynamic programmings are discussed.

scholarly journals Dislocated quasi cone b-metric space over Banach algebra and contraction principles with application to functional equations

2019 ◽  
Vol 17 (1) ◽  
pp. 1065-1081
Author(s):  
Reny George ◽  
Hossam A. Nabwey ◽  
Jelena Vujaković ◽  
R. Rajagopalan ◽  
Selva Vinayagam
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Common Fixed Point ◽  
Metric Space ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Identical Pair ◽  
Common Fixed Point Theorems

Abstract In this paper we introduce dislocated and dislocated quasi version of a cone b-metric space over a Banach algebra as well as weak semi α-admissible and α-identical pair of mappings and prove common fixed point theorems for a pair of α-identical and weak α-admissible mappings in the aforesaid spaces. Our results are supported with suitable examples and an application to a system of m-tupled functional equations.

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.

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