Generalized Hyers-Ulam stability of a general mixed additive-cubic functional equation in quasi-Banach spaces

2011 ◽  
Vol 28 (3) ◽  
pp. 529-560 ◽  
Author(s):  
Tian Zhou Xu ◽  
John Michael Rassias ◽  
Wan Xin Xu
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Ulam Stability ◽  
Cubic Functional Equation

scholarly journals On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation inn-Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Tian Zhou Xu ◽  
John Michael Rassias
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Direct Method ◽  
Ulam Stability ◽  
Cubic Functional Equation ◽  
Cubic Function

The objective of the present paper is to determine the generalized Hyers-Ulam stability of the mixed additive-cubic functional equation inn-Banach spaces by the direct method. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping.

scholarly journals Additive-cubic functional equations from additive groups into non-Archimedean Banach spaces

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 731-738
Author(s):  
Gordji Eshaghi ◽  
Bavand Savadkouhi ◽  
M. Bidkham
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Functional Equations ◽  
Mixed Type ◽  
Ulam Stability ◽  
Cubic Functional Equation

In this paper, we establish the generalized Hyres-Ulam stability of the mixed type additive-cubic functional equation ?(2x + y) + ?(2x - y) = 2? (x + y) + 2?(x - y) + 2?(2x) - 4?(x) from additive groups into non-Archimedean Banach spaces.

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 Hyperstability of the k -Cubic Functional Equation in Non-Archimedean Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Youssef Aribou ◽  
Mohamed Rossafi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
Banach Spaces ◽  
Functional Equations ◽  
Cubic Functional Equation ◽  
Fixed Point Approach ◽  
Fixed Positive Integer

Using the fixed point approach, we investigate a general hyperstability results for the following k -cubic functional equations f k x + y + f k x − y = k f x + y + k f x − y + 2 k k 2 − 1 f x , where k is a fixed positive integer ≥ 2 , in ultrametric Banach spaces.

GENERALIZED HYERS-ULAM STABILITY FOR A GENERAL CUBIC FUNCTIONAL EQUATION IN QUASI-β-NORMED SPACES

2011 ◽  
Vol 04 (03) ◽  
pp. 413-425 ◽  
Author(s):  
G. Z. Eskandani ◽  
J. M. Rassias ◽  
P. Gavruta
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Cubic Functional Equation

In this paper, we investigate the generalized Hyers-Ulam stability of the following general cubic functional equation [Formula: see text] (k ∈ ℕ, k ≠ 1) in quasi-β-normed spaces and by a counterexample, we will show that this functional equation in a special condition is not stabile.

scholarly journals Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
Hark-Mahn Kim
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Banach Spaces ◽  
Mixed Type ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
Linear Spaces ◽  
Quadratic Mappings

we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability inp-Banach spaces.

scholarly journals On the stability problem of quadratic functional equations in 2-Banach spaces

2017 ◽  
pp. 5054-5061
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Stability Problem ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability ◽  
Stability Results

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and G·avruta for the quadratic functional equation:f(2x + y) + f(2x ¡ y) = 2f(x + y) + 2f(x ¡ y) + 4f(x) ¡ 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by thequadratic functional equation in normed spaces to 2-Banach spaces.

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