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 Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Azadi Kenary ◽  
H. Rezaei ◽  
Y. W. Lee ◽  
G. H. Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Mixed Type ◽  
Direct Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Methods ◽  
Rassias Stability

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equationf(x+ky)+f(x−ky)=f(x+y)+f(x−y)+(2(k+1)/k)f(ky)−2(k+1)f(y)for fixed integerskwithk≠0,±1in fuzzy 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.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

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.

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.

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.

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