[PDF] Top 20 Superstability and Stability of the Pexiderized Multiplicative Functional Equation

... for all x, y ∈ S and for a function ϕ : S × S → 0, ∞ with some coditions, then g is bounded or else g is an exponential and h h1g. This is a generalization of the result of Sz´ekelyhidi. Also we investigate the ... See full document

... the superstability of the exponential equation(see also [3, 7, 10] ...the multiplicative property of the norm was ...is multiplicative, ...the multiplicative norm ... See full document

... introduce functional equations of *-derivations and of quadratic ...the stability of *-derivations associated with the Cauchy func- tional equation and the Jensen functional equation ... See full document

... cosine functional equation C, the stability of which is established in the work in ...trigonometric functional equation T, the stability of which is established in ... See full document

... Cauchy functional equations because these are reduced the Cauchy functional equations if g is identically ...Ulam stability or superstability due to the conditions of ...Hyers-Ulam ... See full document

... then either |fx| ≤ 1 √ 1 2ε/2 for all x ∈ G or f is a solution of C. Badora 10 in 1998, and Badora and Ger 11 in 2002 under the condition |f xyfx−y−2fxfy| ≤ ε, ϕx or ϕy, respectively. Also the stability of the ... See full document

... the stability inequalities in all the results of Section 2, then we obtain the same number of corollaries, which are the stability of the hyperbolic cosine type functional equations C λ fg , C λ gf , ... See full document

... It seems that the stability problem of functional equations had been first raised by S. M. Ulam cf. 1, Chapter VI. “For what metric groups G is it true that an ε-automorphism of G is necessarily near to a ... See full document

... of stability problems had been formulated by Ulam in 1 during a talk in 1940: under what condition does there exist a homomorphism near an approximate homomorphism? In the following year 1941, Hyers in 2 has ... See full document

... the stability of the Pexider type functional equation of (FE) added a cocycle property to the conditions in the results [, ...These functional equations arise in the characterization of ... See full document

... In other words, we are looking for situations when the homomorphisms are stable, that is, if a mapping is almost a homomorphism, then there exists a true homomorphism near it. If we turn our attention to the case of ... See full document

... Hyers-Ulam stability problems of functional equations go back to 1940 when Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group (see ...numerous functional ... See full document

... Hyers-Ulam-Rassias stability theorem for the Pexiderized quadratic functional equation ...the stability for odd and even functions and then we apply our results to a general ... See full document

... Hyers-Ulam stability of the Cauchy expo- nential equation f (x + y) = f (x)f ...the functional inequality f (xy) – f (x)f (y) ≤ δ for all x, y ∈ S, then f is either bounded or ... See full document

... Hyers-Ulam stability of a pexiderized quadratic ...The stability problems of several functional equations have been extensively investigated by a number of authors and there are many ... See full document

... Theorem 3.5. Let E be a normed vector space, F a Banach space and f : E → F a mapping which satisfies the inequality (3.10) for some θ ≥ 0, p > 2 and for all x, y ∈ E. Then there exists a unique mapping q : E → F , ... See full document

... Studies on fuzzy normed linear spaces are relatively recent in the field of fuzzy functional analysis. In 1984, Katsaras [14] first introduced the notion of fuzzy norm on a linear space and at the same year Wu and ... See full document

... The method which was provided by Hyers, and which produces the additive mapping h, was called a direct method. This method is the most important and most powerful tool for studying the stability of various ... See full document

... In this paper the stability of quadratic functional equation, f(xy)+f(xy -1 )=2f(x)+2f(y) on class of groups is obtained and also prove that quadratic functional [r] ... See full document

... on Functional Equations asked the question whether such a theorem can also be proved for p ...Hyers-Ulam stability concept. This new concept of stability is known as general- ized Hyers-Ulam ... See full document