scholarly journals Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1050 ◽  
Author(s):  
Abdulaziz M. Alanazi ◽  
G. Muhiuddin ◽  
K. Tamilvanan ◽  
Ebtehaj N. Alenze ◽  
Abdelhalim Ebaid ◽  
...  
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Normed Space ◽  
Additive Functional ◽  
Current Work ◽  
Ulam Stability ◽  
Fuzzy Normed Space ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Stability Results

In this current work, we introduce the finite variable additive functional equation and we derive its solution. In fact, we investigate the Hyers–Ulam stability results for the finite variable additive functional equation in fuzzy normed space by two different approaches of direct and fixed point methods.

scholarly journals Hyers–Ulam Stability of Additive Functional Equation Using Direct and Fixed-Point Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
K. Tamilvanan ◽  
G. Balasubramanian ◽  
Nazek Alessa ◽  
K. Loganathan
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonnegative Integer ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Stability Results

In this present work, we obtain the solution of the generalized additive functional equation and also establish Hyers–Ulam stability results by using alternative fixed point for a generalized additive functional equation χ ∑ g = 1 l v g = ∑ 1 ≤ g < h < i ≤ l χ v g + v h + v i − ∑ 1 ≤ g < h ≤ l χ v g + v h − l 2 − 5 l + 2 / 2 ∑ g = 1 l χ v g − χ − v g / 2 . where l is a nonnegative integer with ℕ − 0,1,2,3,4 in Banach spaces.

scholarly journals On the non-Archimedean and random approximately general additive mappings: Direct and fixed point methods

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1753-1771
Author(s):  
Azadi Kenary ◽  
M.H. Eghtesadifard
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
Additive Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Additive Mappings

In this paper, we prove the Hyers-Ulam stability of the following generalized additive functional equation ?1? i < j ? m f(xi+xj/2 + m-2?l=1,kl?i,j) = (m-1)2/2 m?i=1 f(xi) where m is a positive integer greater than 3, in various normed spaces.

scholarly journals Approximation of Homomorphisms and Derivations on non-Archimedean LieC∗-Algebras via Fixed Point Method

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yeol Je Cho ◽  
Reza Saadati ◽  
Javad Vahidi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Fixed Point Methods

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms inC∗-algebras and LieC∗-algebras and of derivations on non-ArchimedeanC∗-algebras and Non-Archimedean LieC∗-algebras for anm-variable additive functional equation.

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 the Stability of -Derivations and Lie -Algebra Homomorphisms on Lie -Algebras: A Fixed Points Method

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Fixed Points ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
The Stability ◽  
Algebra Homomorphisms ◽  
Stability Results

We investigate new generalized Hyers-Ulam stability results for -derivations and Lie -algebra homomorphisms on Lie -algebras associated with the additive functional equation:

scholarly journals Fixed Points and Stability of an Additive Functional Equation ofn-Apollonius Type inC∗-Algebras

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Fridoun Moradlou ◽  
Hamid Vaezi ◽  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Generalized Derivations ◽  
Additive Functional Equation ◽  
Algebra Homomorphisms

Using the fixed point method, we prove the generalized Hyers-Ulam stability ofC∗-algebra homomorphisms and of generalized derivations onC∗-algebras for the following functional equation of Apollonius type∑i=1nf(z−xi)=−(1/n)∑1≤i<j≤nf(xi+xj)+nf(z−(1/n2)∑i=1nxi).

STABILITY ANALYSIS IN BANACH SPACES FOR A GENERAL ADDITIVE FUNCTIONAL EQUATION

2020 ◽  
Vol 9 (11) ◽  
pp. 9179-9186
Author(s):  
P. Agilan ◽  
J.M. Rassias ◽  
V. Vallinayagam
Keyword(s):  
Functional Equation ◽  
Stability Analysis ◽  
Banach Spaces ◽  
Direct Method ◽  
Additive Functional ◽  
Ulam Stability ◽  
General Control ◽  
Additive Functional Equation ◽  
Control Functions ◽  
Stability Results

In this paper, we present the Hyers-Ulam stability of generalized additive functional equation in Banach spaces and stability results have been obtained by a classical direct method by various general control functions.

scholarly journals Generalized Hyers-Ulam stability for general additive functional equations on non-Archimedean random lie C*-algebras

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2127-2138
Author(s):  
Zhihua Wang ◽  
Prasanna Sahoo
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Fixed Integer ◽  
Additive Functional Equation ◽  
C Algebras

In this paper, using the fixed point method, we prove some results related to the generalized Hyers-Ulam stability of homomorphisms and derivations in non-Archimedean random C*-algebras and non-Archimedean random Lie C*-algebras for the generalized additive functional equation ?1 ? i < j ?n f(xi+xj/2 + ?n-2 l=1,kl?i,j xkl) = (n-1)2/2 ?n,i=1 f(xi) where n ? N is a fixed integer with n ? 3.

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