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APPROXIMATE J¤-DERIVATIONS ON J¤-ALGEBRAS
Hark-Mahn Kim,Sanghoon Lee 충청수학회 2011 충청수학회지 Vol.24 No.2
We establish alternative stability and superstability ofJ¤-derivations in J¤-algebras for a generalized Jensen type func- tional equation by using the direct method and the ¯xed point alternative method.
ADDITIVE FUNCTIONAL EQUATION WITH SEVERAL VARIABLES AND ITS STABILITY
Hark-Mahn Kim,Hwan-Yong Shin 충청수학회 2014 충청수학회지 Vol.27 No.3
In this paper, we prove the generalized Hyers{Ulam stability of an n-dimensional additive functional equation, and then apply stability results to Banach modules over a unital Banach algebras.
STABILITY OF FUNCTIONAL EQUATION AND INEQUALITY IN FUZZY NORMED SPACES
Hark-Mahn Kim,Yang-Hi Lee 충청수학회 2013 충청수학회지 Vol.26 No.4
In this paper, we investigate a fuzzy version of stability theory for the following functional equation f(x + y) + f(x ¡ y) ¡ 2f(x) ¡ f(y) ¡ f(¡y) = 0 in the sense of M. Mirmostafaee and M. S. Moslehian.
Hark-Mahn Kim,Kil-Woung Jun,Ahyoung Kim 충청수학회 2013 충청수학회지 Vol.26 No.2
The main goal of this paper is to present the addi-tional stability results of the following orthogonally additive and orthogonally quadratic functional equation f(x2+ y) + f(x2¡ y) + f(x2+ z) + f(x2¡ z)=32 f(x) ¡12 f(¡x) + f(y) + f(¡y) + f(z) + f(¡z); for all x; y; z with x ? y, which has been introduced in the pa- per [11], in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.
Stability of the Functional Equations related to a Multiplicative Derivation
Hark-Mahn Kim,Ick-Soon Chang 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.11 No.1-2
In this paper, using an idea from the direct method of Hyers and Ulam,we investigate the situations so that the Hyers-Ulam-Rassias stability of the func-tional equation g(x2) = 2 xg(x) is satised.AMS Mathematics Subject Classication : 39B52, 39B72.Key words and phrases : Hyers-Ulam stability, multiplicative derivation1. IntroductionIn 1940, S. M. Ulam [14] gave a wide ranging talk before the mathematicsclub of the University of Wisconsin in which he discussed a number of importantunsolved problems. Among those was the question concerning the stability ofgroup homomorphisms:LetG1 be a group and letG2 be a metric group with the metricd(·,·). Given0, does there exist a 0 such that if a functionh :G1 → G2 satises theinequality d(h(xy),h(x)h(y)) for allx,y∈G1, then there exists a homomor-phism H :G1 → G2 withd(h(x),H(x)) for allx ∈G1?In other words, we are looking for situations when the homomorphisms are
ON THE STABILITY OF A MODIFIED JENSEN TYPE CUBIC MAPPING
Hark Mahn Kim,Hoon Ko,Ji ae Son 충청수학회 2008 충청수학회지 Vol.21 No.1
In this paper we introduce a Jensen type cubic functional equation f3x + y2+ fx + 3y2= 12fx + y2+ 2f(x) + 2fy),and then investigate the generalized Hyers–Ulam stability problem for the equation.
HYERS{ULAM STABILITY OF FUNCTIONAL INEQUALITIES ASSOCIATED WITH CAUCHY MAPPINGS
Hark Mahn Kim,Jeong Ha Oh 충청수학회 2007 충청수학회지 Vol.20 No.4
In this paper, we investigate the generalized Hyers{Ulam stability of the functional inequality kaf(x) + bf(y) + cf(z)k · kf(ax + by + cz))k + Á(x; y; z)associated with Cauchy additive mappings. As a result, we obtain that if a mapping satis¯es the functional inequality with perturbing term which satis¯es certain conditions then there exists a Cauchy additive mapping near the mapping.
Stability of Approximate Quadratic Mappings
Kim, Hark-Mahn,Kim, Minyoung,Lee, Juri Hindawi Publishing Corporation 2010 Journal of inequalities and applications Vol.2010 No.1
<P>We investigate the general solution of the quadratic functional equation f(2x+y)+3f(2x-y)=4f(x-y)+12f(x), in the class of all functions between quasi-β-normed spaces, and then we prove the generalized Hyers-Ulam stability of the equation by using direct method and fixed point method.</P>