scholarly journals Stability of the Apollonius Type Additive Functional Equation in Modular Spaces and Fuzzy Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1125 ◽  
Author(s):  
Sang Og Kim ◽  
John Michael Michael Rassias
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Integral Equations ◽  
Banach Algebras ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Modular Spaces ◽  
Jordan Triple Product ◽  
Differential And Integral Equations

In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without Δ 2 -conditions. We study the same problem in fuzzy Banach spaces and β -homogeneous Banach spaces. We show the hyperstability of the functional equation associated with the Jordan triple product in fuzzy Banach algebras. The obtained results can be applied to differential and integral equations with kernels of non-power types.

scholarly journals Hyers-Ulam stability of a finite variable mixed type quadratic-additive functional equation in quasi-Banach spaces

2020 ◽  
Vol 5 (6) ◽  
pp. 5993-6005 ◽  
Author(s):  
K. Tamilvanan ◽  
◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
◽  
...  
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Mixed Type ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation

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.

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 A fixed point approach to the fuzzy stability of an AQCQ-functional equation

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1833-1851 ◽  
Author(s):  
Choonkil Park ◽  
Dong Shin ◽  
Reza Saadati ◽  
Jung Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Stability Problems ◽  
Fixed Point Approach ◽  
Quartic Functional Equation

In [32, 33], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. Using the fixed point method, we prove the Hyers-Ulam stability of the following additive-quadraticcubic-quartic functional equation f(x+2y)+f(x-2y)=4f(x+y)+4f(x-y)-6f(x)+f(2y)+f(-2y)-4f(y)-4f(-y) (1) in fuzzy Banach spaces.

scholarly journals Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Topological Structure ◽  
Continued Fraction ◽  
Additive Functional ◽  
Analytic Structure ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Analytical Structure ◽  
Knots And Links

We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. As applications of the analytical structure, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional equation fx⊕y=fx⊕fy in tangle space which is a set of real tangles with analytic structure and describe the DNA recombination as the action of some enzymes on tangle space.

scholarly journals Generalized Hyers–Ulam Stability of the Additive Functional Equation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 76 ◽  
Author(s):  
Yang-Hi Lee ◽  
Gwang Kim
Keyword(s):  
Functional Equation ◽  
Additive Function ◽  
Additive Functional ◽  
Stability Theorem ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Stability Theorems ◽  
The Stability

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations.

scholarly journals Local stability of the additive functional equation and its applications

2003 ◽  
Vol 2003 (1) ◽  
pp. 15-26 ◽  
Author(s):  
Soon-Mo Jung ◽  
Byungbae Kim
Keyword(s):  
Functional Equation ◽  
Large Class ◽  
Local Stability ◽  
Unbounded Domains ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Jensen’S Functional Equation ◽  
Restricted Domains ◽  
The Stability

The main purpose of this paper is to prove the Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains. Furthermore, by using the theorem, we prove the stability of Jensen's functional equation for a large class of restricted domains.

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