scholarly journals Equalities and inequalities for several variables mappings

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Single Equation ◽  
Ulam Stability ◽  
Systems Of Equations ◽  
Normed Spaces ◽  
Mild Conditions ◽  
Several Variables

AbstractIn this paper, some special mappings of several variables such as the multicubic and the multimixed quadratic–cubic mappings are introduced. Then, the systems of equations defining a multicubic and a multimixed quadratic–cubic mapping are unified to a single equation. Under some mild conditions, it is shown that a multimixed quadratic–cubic mapping can be multiquadratic, multicubic and multiquadratic–cubic. Furthermore, by applying a known fixed-point theorem, the Hyers–Ulam stability of multimixed quadratic–cubic, multiquadratic, multicubic and multiquadratic–cubic are studied in non-Archimedean normed spaces.

scholarly journals Approximate multi-Jensen-cubic mappings and a fixed point theorem

2020 ◽  
Vol 19 (1) ◽  
pp. 141-154
Author(s):  
Elahe Ramzanpour ◽  
Abasalt Bodaghi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Single Equation ◽  
Ulam Stability ◽  
System Of Functional Equations

AbstractIn this paper, we introduce multi-Jensen-cubic mappings and unify the system of functional equations defining the multi-Jensen-cubic mapping to a single equation. Applying a fixed point theorem, we establish the generalized Hyers-Ulam stability of multi-Jensen-cubic mappings. As a known outcome, we show that every approximate multi-Jensen-cubic mapping can be multi-Jensen-cubic.

scholarly journals Characterization, stability and hyperstability of multi-quadratic–cubic mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abasalt Bodaghi ◽  
Ajda Fošner
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Single Equation ◽  
Ulam Stability ◽  
System Of Functional Equations

AbstractIn this paper, we unify the system of functional equations defining a multi-quadratic–cubic mapping to a single equation. Applying a fixed point theorem, we study the generalized Hyers–Ulam stability of multi-quadratic–cubic mappings. As a result, we investigate the hyperstability of multi-quadratic–cubic mappings in some senses.

HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

2020 ◽  
Vol 102 (2) ◽  
pp. 293-302
Author(s):  
THEERAYOOT PHOCHAI ◽  
SATIT SAEJUNG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Linear Functional ◽  
Linear Equations ◽  
General Linear ◽  
Several Variables ◽  
Linear Functional Equations

Zhang [‘On hyperstability of generalised linear functional equations in several variables’, Bull. Aust. Math. Soc.92 (2015), 259–267] proved a hyperstability result for generalised linear functional equations in several variables by using Brzdęk’s fixed point theorem. We complete and extend Zhang’s result. We illustrate our results for general linear equations in two variables and Fréchet equations.

ON APPROXIMATELY ADDITIVE MAPPINGS IN 2-BANACH SPACES

2019 ◽  
Vol 101 (2) ◽  
pp. 299-310 ◽  
Author(s):  
JANUSZ BRZDĘK ◽  
EL-SAYED EL-HADY
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Stability Result ◽  
Main Tool ◽  
Ulam Stability ◽  
Cauchy Equation ◽  
Stability Issues ◽  
Additive Mappings

We show how some Ulam stability issues can be approached for functions taking values in 2-Banach spaces. We use the example of the well-known Cauchy equation $f(x+y)=f(x)+f(y)$, but we believe that this method can be applied for many other equations. In particular we provide an extension of an earlier stability result that has been motivated by a problem of Th. M. Rassias. The main tool is a recent fixed point theorem in some spaces of functions with values in 2-Banach spaces.

scholarly journals Onn-normed spaces

2001 ◽  
Vol 27 (10) ◽  
pp. 631-639 ◽  
Author(s):  
Hendra Gunawan ◽  
M. Mashadi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Normed Space ◽  
Normed Spaces

Given ann-normed space withn≥2, we offer a simple way to derive an(n−1)-norm from then-norm and realize that anyn-normed space is an(n−1)-normed space. We also show that, in certain cases, the(n−1)-norm can be derived from then-norm in such a way that the convergence and completeness in then-norm is equivalent to those in the derived(n−1)-norm. Using this fact, we prove a fixed point theorem for somen-Banach spaces.

scholarly journals Fixed Point Theorem on Contractive Mapping in Standard 2-Normed Spaces

2021 ◽  
Vol 18 (1) ◽  
pp. 93-101
Author(s):  
Salsabila Ammari ◽  
Muh Nur ◽  
Naimah Aris
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Contractive Mapping ◽  
Normed Spaces ◽  
The Fixed Point Theorem

This paper discussed about the proof of the fixed point theorem on the standard 2-normed spaces by using completeness. The completeness of the standard 2-normed spaces is shown by defining a new norm. Two linear independent vectors on standard 2-normed spaces are used to define the new norm, namely  which has been shown to be equivalent to standard norm.

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