A Fixed Point Approach to the Stability of a General Mixed AQCQ-Functional Equation in Non-Archimedean Normed Spaces

Using the fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equationf(x+ky)+f(x−ky)=k2f(x+y)+k2f(x−y)+2(1−k2)f(x)+((k4−k2)/12)[f(2y)+f(−2y)−4f(y)−4f(−y)]for a fixed integerkwithk≠0,±1 in non-Archimedean normed spaces.

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Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

Abstract and Applied Analysis ◽

10.1155/2010/849543 ◽

2010 ◽

Vol 2010 ◽

pp. 1-15 ◽

Cited By ~ 2

Author(s):

Choonkil Park

Keyword(s):

Functional Equation ◽

Fixed Point ◽

Fixed Points ◽

Banach Spaces ◽

Fixed Point Method ◽

Point Method ◽

Ulam Stability ◽

Normed Spaces ◽

Quartic Functional Equation ◽

The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

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The Stability Analysis of A-Quartic Functional Equation

Mathematics ◽

10.3390/math9222881 ◽

2021 ◽

Vol 9 (22) ◽

pp. 2881

Author(s):

Chinnaappu Muthamilarasi ◽

Shyam Sundar Santra ◽

Ganapathy Balasubramanian ◽

Vediyappan Govindan ◽

Rami Ahmad El-Nabulsi ◽

...

Keyword(s):

Functional Equation ◽

Fixed Point ◽

Stability Analysis ◽

General Solution ◽

Banach Spaces ◽

Ulam Stability ◽

Quartic Functional Equation ◽

Fixed Point Methods ◽

The Stability

In this paper, we study the general solution of the functional equation, which is derived from additive–quartic mappings. In addition, we establish the generalized Hyers–Ulam stability of the additive–quartic functional equation in Banach spaces by using direct and fixed point methods.

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Nonlinear Random Stability via Fixed-Point Method

Journal of Applied Mathematics ◽

10.1155/2012/902931 ◽

2012 ◽

Vol 2012 ◽

pp. 1-45 ◽

Cited By ~ 2

Author(s):

Yeol Je Cho ◽

Shin Min Kang ◽

Reza Saadati

Keyword(s):

Functional Equation ◽

Fixed Point ◽

Fixed Point Method ◽

Point Method ◽

Ulam Stability ◽

Normed Spaces ◽

Quartic Functional Equation ◽

Random Normed Spaces

We prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in various complete random normed spaces.

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A fixed point approach to the stability of a septic functional equation in fuzzy quasi-β-normed spaces

Journal of Intelligent & Fuzzy Systems ◽

10.3233/ifs-141328 ◽

2015 ◽

Vol 28 (2) ◽

pp. 513-523 ◽

Cited By ~ 1

Author(s):

Yonghong Shen ◽

Wei Chen ◽

Yaoyao Lan

Keyword(s):

Functional Equation ◽

Fixed Point ◽

Normed Spaces ◽

Fixed Point Approach ◽

The Stability

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A Fixed Point Approach To The Stability Of A Mixed Quadratic-Quartic (QQ) Functional Equation In Quasi−Β−Normed Spaces

International Journal of Mathematics Trends and Technology ◽

10.14445/22315373/ijmtt-v20p504 ◽

2015 ◽

Vol 20 (1) ◽

pp. 25-40

Author(s):

K Balamurugan ◽

◽

M Arunkumar ◽

P Ravindiran

Keyword(s):

Functional Equation ◽

Fixed Point ◽

Normed Spaces ◽

Fixed Point Approach ◽

The Stability

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A fixed point approach to the stability of a general quartic functional equation

Journal of Mathematics and Computer Science ◽

10.22436/jmcs.020.03.03 ◽

2019 ◽

Vol 20 (03) ◽

pp. 207-215 ◽

Cited By ~ 3

Author(s):

Yang-Hi Lee ◽

Soon-Mo Jung

Keyword(s):

Functional Equation ◽

Fixed Point ◽

Fixed Point Approach ◽

Quartic Functional Equation ◽

The Stability

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A FIXED POINT APPROACH TO THE STABILITY OF GENERAL QUADRATIC EULER-LAGRANGE FUNCTIONAL EQUATIONS IN INTUITIONISTIC FUZZY SPACES

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v12i4.4424 ◽

2016 ◽

pp. 4430-4436

Author(s):

Seong Sik Kim ◽

Ga Ya Kim

Keyword(s):

Fixed Point ◽

Functional Equations ◽

Fixed Point Method ◽

Ulam Stability ◽

Normed Spaces ◽

Fixed Point Approach ◽

Intuitionistic Fuzzy ◽

The Stability ◽

Lagrange Functional ◽

Intuitionistic Fuzzy Normed Spaces

In this paper, we prove the generalized Hyers-Ulam stability of a general k-quadratic Euler-Lagrange functional equation:for any fixed positive integerÂ in intuitionistic fuzzy normed spaces using a fixed point method.

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A fixed point approach to the stability of a quadratic-additive type functional equation in non-Archimedean normed spaces

International Journal of Mathematical Analysis ◽

10.12988/ijma.2015.53100 ◽

2015 ◽

Vol 9 ◽

pp. 1477-1487

Author(s):

Sun-Sook Jin ◽

Yang-Hi Lee

Keyword(s):

Functional Equation ◽

Fixed Point ◽

Normed Spaces ◽

Fixed Point Approach ◽

Additive Type ◽

The Stability

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A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Functional Equation

Fixed Point Theory and Applications ◽

10.1155/2010/185780 ◽

2010 ◽

Vol 2010 ◽

pp. 1-17 ◽

Cited By ~ 2

Author(s):

Jung Rye Lee ◽

Ji-hye Kim ◽

Choonkil Park

Keyword(s):

Functional Equation ◽

Fixed Point ◽

Fixed Point Approach ◽

Quartic Functional Equation ◽

The Stability

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

Filomat ◽

10.2298/fil1409753k ◽

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.

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