scholarly journals Introducing of an orthogonally relation for stability of ternary cubic homomorphisms and derivations on C*-ternary algebras

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1439-1445
Author(s):  
M. Rabbani ◽  
M. Eshaghi
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Metric Spaces ◽  
Control Function ◽  
Fixed Point Method ◽  
Continuous Maps ◽  
Ternary Algebras ◽  
The Fixed Point Theorem ◽  
The Stability ◽  
Contraction Maps

In this article, weintroduce a kind of binary relation on a nonempty set with name of orthogonally relation which we develop for sequences, continuous maps, metric spaces, contraction maps, preserving maps and etc. All of the above concepts are generalized forms of ordinary case, so they are very important for extension and finding new results. we expect some of the concepts in the mathematics can be changed by orthogonally relation, such as functional equations and some of the theorem in the fixed point theorem method. In this research we illustrate one of the applications of orthogonally relation on ternary cubic homomorphism and ternary cubic derivations, so we prove the stability of orthogonally ternary cubic homomorphisms and orthogonally ternary cubic derivations on C*-ternary algebras for the functional equation by using fixed point method. Also to create the stability, we choose a suitable control function and we show ability and validity of the proposed method for the functional analysis.

A FIXED POINT APPROACH TO THE STABILITY OF GENERAL QUADRATIC EULER-LAGRANGE FUNCTIONAL EQUATIONS IN INTUITIONISTIC FUZZY SPACES

2016 ◽  
pp. 4430-4436
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Fixed Point Approach ◽  
Intuitionistic Fuzzy ◽  
The Stability ◽  
Lagrange Functional ◽  
Intuitionistic Fuzzy Normed Spaces

In this paper, we prove the generalized Hyers-Ulam stability of a general k-quadratic Euler-Lagrange functional equation:for any fixed positive integer in intuitionistic fuzzy normed spaces using a fixed point method.

A Fixed Point Approach to the Stability of Quadratic Functional Equations in Modular Spaces

2017 ◽  
Vol 6 (1) ◽  
pp. 171-175
Author(s):  
Seong Sik Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
Modular Spaces ◽  
The Stability ◽  
Positive Integers ◽  
Rassias Stability

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equation f(kx + y) + f(kx – y) = 2k2f(x) + 2f(y) for any fixed positive integers k ∈ Ζ+ in modular spaces by using fixed point method.

scholarly journals Fixed-Point Theorem for Multivalued Quasi-Contraction Maps in a V-Fuzzy Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Matthew Brijesh Sookoo ◽  
Sreedhara Rao Gunakala
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric ◽  
The Fixed Point Theorem ◽  
Contraction Maps

In this paper, we introduce the concept of a set-valued or multivalued quasi-contraction mapping in V-fuzzy metric spaces. Using this new concept, a fixed-point theorem is established. We also provide an example verifying and illustrating the fixed-point theorem in action.

Non-Archimedean hyperstability of Cauchy–Jensen functional equations on a restricted domain

2018 ◽  
Vol 24 (2) ◽  
pp. 155-165
Author(s):  
Iz-iddine EL-Fassi
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Metric Spaces ◽  
Fixed Point Approach ◽  
Nonlinear Anal ◽  
Stability Of Functional Equations ◽  
Jensen Functional ◽  
Empty Subset ◽  
The Stability ◽  
Fixed Positive Integer

Abstract Let X be a normed space, {U\subset X\setminus\{0\}} a non-empty subset, and {(G,+)} a commutative group equipped with a complete ultrametric d that is invariant (i.e., {d(x+z,y+z)=d(x,y} ) for {x,y,z\in G} ). Under some weak natural assumptions on U and on the function {\gamma\colon U^{3}\to[0,\infty)} , we study the new generalized hyperstability results when {f\colon U\to G} satisfies the inequality d\biggl{(}\alpha f\biggl{(}\frac{x+y}{\alpha}+z\biggr{)},\alpha f(z)+f(y)+f(x)% \biggr{)}\leq\gamma(x,y,z) for all {x,y,z\in U} , where {\frac{x+y}{\alpha}+z\in U} and {\alpha\geq 2} is a fixed positive integer. The method is based on a quite recent fixed point theorem (Theorem 1 in [J. Brzdȩk and K. Ciepliński, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Anal. 74 2011, 18, 6861–6867]) (cf. [8, Theorem 1]) in some functions spaces.

scholarly journals Ulam stability of functional equations in 2-Banach spaces via the fixed point method

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Krzysztof Ciepliński
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Several Variables ◽  
Stability Of Functional Equations ◽  
Special Cases ◽  
The Stability

AbstractUsing the fixed point method, we prove the Ulam stability of two general functional equations in several variables in 2-Banach spaces. As corollaries from our main results, some outcomes on the stability of a few known equations being special cases of the considered ones will be presented. In particular, we extend several recent results on the Ulam stability of functional equations in 2-Banach spaces.

scholarly journals Approximately Quintic and Sextic Mappings Formr-Divisible Groups into Ŝerstnev Probabilistic Banach Spaces: Fixed Point Method

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
Y. J. Cho ◽  
M. B. Ghaemi ◽  
H. Majani
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Constant Coefficients ◽  
The Stability ◽  
Divisible Groups

Using the fixed point method, we investigate the stability of the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients formr-divisible groups into Ŝerstnev probabilistic Banach spaces.

scholarly journals A New Coupled Fixed Point Result in Extended Metric Spaces with an Application to Study the Stability of Set-Valued Functional Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Ahmed H. Soliman ◽  
A. M. Zidan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Functional Equations ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Generalized Metric Space ◽  
Coupled Fixed Point Theorem ◽  
The Stability

In this paper, we introduce a new coupled fixed point theorem in a generalized metric space and utilize the same to study the stability for a system of set-valued functional equations.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

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