• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.149-159
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• 2022

In this note, we prove some theorems concerning the stability of functional inequality associated with additive mappings on quasi-𝛽-normed spaces.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1421-1433
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• 2011

In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${\beta}$-normed space and ${\sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.319-326
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• 2020

In this paper, we establish a general solution of the following functional equation $$mf\({\sum\limits_{k=1}^{n}}x_k\)+{\sum\limits_{t=1}^{m}}f\({\sum\limits_{k=1}^{n-i_t}}x_k-{\sum\limits_{k=n-i_t+1}^{n}}x_k\)=2{\sum\limits_{t=1}^{m}}\(f\({\sum\limits_{k=1}^{n-i_t}}x_k\)+f\({\sum\limits_{k=n-i_t+1}^{n}}x_k\)\)$$ where m, n, t, i_t ∈ ℕ such that 1 ≤ t ≤ m < n. Also, we study Hyers-Ulam-Rassias stability for the generalized quadratic functional equation with n-variables and m-combinations form in quasi-𝛽-normed spaces and then we investigate its application.

• The Pure and Applied Mathematics
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• v.26 no.2
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• pp.85-97
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• 2019

In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.691-700
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• 2009

We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.757-767
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• 2013

We investigate the general solution of the following functional equation and the generalized Hyers-Ulam-Rassias stability problem in quasi ${\beta}$-normed spaces and then the stability by using alternative fixed point method for the following quintic function $f:X{\rightarrow}Y$ such that f(3x+y)+f(3x-y)+5[f(x+y)+f(x-y)]=4[f(2x+y)+f(2x-y)]+2f(3x)-246f(x), for all $x,y{\in}X$.

• The Mathematical Education
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• v.21 no.1
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• pp.41-44
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• 1982

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.509-524
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• 2023

In this study, we characterize the structure of the multivariable mappings which are sextic in each component. Indeed, we unify the general system of multi-sextic functional equations defining a multi-sextic mapping to a single equation. We also establish the Hyers-Ulam and Găvruţa stability of multi-sextic mappings by a fixed point theorem in non-Archimedean normed spaces. Moreover, we generalize some known stability results in the setting of quasi-𝛽-normed spaces. Using a characterization result, we indicate an example for the case that a multi-sextic mapping is non-stable.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.401-411
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• 2014

In this paper, we prove the generalized Hyers-Ulam stability of the following Jensen type functional equation $$f(\frac{x-y}{n}+z)+f(\frac{y-z}{n}+x)+f(\frac{z-x}{n}+y)=f(x)+f(y)+f(z)$$ in p-Banach spaces for any fixed nonzero integer n.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.601-606
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• 2008

The purpose of this paper is to introduce and discuss the concept of ${\omega}$-Chebyshev subspaces in Banach spaces. The concept of quasi Chebyshev in Banach space is defined. We show that ${\omega}$-Chebyshevity of subspaces are a new class in approximation theory. In this paper, also we consider orthogonality in normed spaces.