scholarly journals An improvement result concerning fixed point theory for cyclic contractions

2016 ◽  
Vol 32 (3) ◽  
pp. 339-347
Author(s):  
MOHAMED JLELI ◽  
◽  
BESSEM SAMET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
System Of Functional Equations ◽  
Cyclic Contractions ◽  
Closure Assumption

In this note, we obtain an improvement result for cyclic contractions by weakening the closure assumption that is usually supposed in the literature. We present some applications of the obtained result to prove the existence of solutions for a system of functional equations.

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.

Coupled fractional differential systems with random effects in Banach spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
O. Zentar ◽  
M. Ziane ◽  
S. Khelifa
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Random Differential Equations ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Vector Valued ◽  
Abstract Formulation

Abstract The purpose of this work is to investigate the existence of solutions for a system of random differential equations involving the Riemann–Liouville fractional derivative. The existence result is established by means of a random abstract formulation to Sadovskii’s fixed point theorem principle [A. Baliki, J. J. Nieto, A. Ouahab and M. L. Sinacer, Random semilinear system of differential equations with impulses, Fixed Point Theory Appl. 2017 2017, Paper No. 27] combined with a technique based on vector-valued metrics and convergent to zero matrices. An example is also provided to illustrate our result.

Fixed point theory for cyclic -contractions

2010 ◽  
Vol 72 (3-4) ◽  
pp. 1181-1187 ◽  
Author(s):  
Mădălina Păcurar ◽  
Ioan A. Rus
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cyclic Contractions

scholarly journals On the Generalized Ulam-Hyers-Rassias Stability of Quadratic Mappings in Modular Spaces withoutΔ2-Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Kittipong Wongkum ◽  
Parin Chaipunya ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Lower Semicontinuous ◽  
Point Theory ◽  
Quadratic Functional ◽  
Modular Spaces ◽  
Quadratic Mappings ◽  
Rassias Stability

We approach the generalized Ulam-Hyers-Rassias (briefly, UHR) stability of quadratic functional equations via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces whose modulars are lower semicontinuous (briefly, lsc) but do not satisfy any relatives ofΔ2-conditions.

On the stability of some functional equations in Menger φ-normed spaces

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Dorel Miheţ ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
The Stability ◽  
Stability Results

AbstractRecently, the authors [MIHEŢ, D.—SAADATI, R.—VAEZPOUR, S. M.: The stability of an additive functional equation in Menger probabilistic φ-normed spaces, Math. Slovaca 61 (2011), 817–826] considered the stability of an additive functional in Menger φ-normed spaces. In this paper, we establish some stability results concerning the cubic, quadratic and quartic functional equations in complete Menger φ-normed spaces via fixed point theory.

scholarly journals On Maximal Elements with Applications to Abstract Economies, Fixed Point Theory and Eigenvector Problems

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 789
Author(s):  
Liang-Ju Chu ◽  
Wei–Shih Du
Keyword(s):  
Fixed Point ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Abstract Economies ◽  
Coercive Condition ◽  
General Abstract

Two existence theorems of maximal elements in H-spaces are obtained without compactness. More accurately, we deal with the correspondence to be of L -majorized mappings in the setting of noncompact strategy sets but merely requiring a milder coercive condition. As applications, we obtain an equilibrium existence theorem for general abstract economies, a new fixed point theorem, and give a sufficient condition for the existence of solutions of the eigenvector problem (EIVP).

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 Existence Results for a System of Coupled Hybrid Differential Equations with Fractional Order

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Mohamed Hannabou ◽  
Khalid Hilal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Result ◽  
Existence Results ◽  
Fractional Differential ◽  
Hybrid Differential Equations

This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example.

scholarly journals Fuzzy Fixed Point Results in F-Metric Spaces with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Monairah Alansari ◽  
Shehu Shagari Mohammed ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cauchy Problems ◽  
Research Directions ◽  
New Research ◽  
Fuzzy Fixed Point

In this paper, some concepts of F-metric spaces are used to study a few fuzzy fixed point theorems. Consequently, corresponding fixed point theorems of multivalued and single-valued mappings are discussed. Moreover, one of our obtained results is applied to establish some conditions for existence of solutions of fuzzy Cauchy problems. It is hoped that the established ideas in this work will awake new research directions in fuzzy fixed point theory and related hybrid models in the framework of F-metric spaces.

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