Stability and non-stability of generalized radical cubic functional equation in quasi-$\beta$-Banach spaces

2019 ◽  
Vol 12 (3) ◽  
pp. 175-190
Author(s):  
Iz-iddine EL-Fassi ◽  
John Michael Rassias
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Cubic 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.

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 A Remark for the Hyers–Ulam Stabilities on n-Banach Spaces

Axioms ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 2
Author(s):  
Jaeyoo Choy ◽  
Hahng-Yun Chu ◽  
Ahyoung Kim
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Banach Spaces ◽  
Functional Equations ◽  
Cubic Functional Equation ◽  
Quartic Functional Equation ◽  
Surjective Mapping

In this article, we deal with stabilities of several functional equations in n-Banach spaces. For a surjective mapping f into a n-Banach space, we prove the generalized Hyers–Ulam stabilities of the cubic functional equation and the quartic functional equation for f in n-Banach spaces.

Stabilities of a general k-cubic functional equation in Banach spaces

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Krishnan Ravi ◽  
Matina J. Rassias ◽  
Pasupathi Narasimman ◽  
Ravi K. Kumar
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Cubic Functional Equation

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.

Orthogonal stability of mixed type additive-cubic functional equations in multi-Banach spaces

2018 ◽  
Vol 51 (1) ◽  
pp. 106-111
Author(s):  
Ramdoss Murali ◽  
Sandra Pinelas ◽  
Aruldass Antony Raj
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Functional Equations ◽  
Mixed Type ◽  
Cubic Functional Equation

Abstract In this paper, we establish the Hyers-Ulam orthogonal stability of the mixed type additive-cubic functional equation in multi-Banach spaces.

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