[PDF] Top 20 10. Generalized Hyers-Ulam stability of a 2-variable reciprocal functional equation

... ≤ 2 −𝑛 𝜙(2 −𝑛 𝑥, 2 −𝑛 𝑢, 2 −𝑛 𝑦, 2 −𝑛 ...unique 2-variable reciprocal function satisfying ...𝑋 2 → 𝑌 be another 2-variable reciprocal ... See full document

... [2] generalized the Hyers theorem for additive ...a generalized version of the theorem of Hyers which permitted the cauchy difference to become ... See full document

... the generalized Hyers-Ulam stability of Hyers- Ulam-Rassias stability of functional ...A generalized and modified form of the theorem evolved by ...to ... See full document

... Note that in Propositions and 2, only the function Ax has been used, so they are stability theorems in the sense of Hyers-Ulam for the functional equation in a single variable 2.7.. The [r] ... See full document

... We claim that the additive functional equation (1.1) is not stable for s = 1 in condition (ii) Corollary 3.1. Suppose on the contrary that there exist a additive mapping A : K 2 → K and a constant ρ ... See full document

... 9. Hyers, DH: On the stability of the linear functional ...(1941) 10. Aoki, T: On the stability of the linear transformation in Banach ...Jpn. 2, 64-66 (1950) 11. Rassias, TM: On ... See full document

... In this section, using a fixed point alternative approach, we prove the generalized Hyers- Ulam stability of the functional equation (.) in non-Archimedean normed spaces. ... See full document

... The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [3, 7, 8, 9, 10, ... See full document

... the Hyers-Ulam stability of the differential equation of the form ty 00 (t) + αty 0 (t) + β y(t) = ...the; Hyers-Ulam-Rassias stability of linear differential equations of ... See full document

... Menger proposed transferring the probabilistic notions of quantum mechanic from physics to the underlying geometry. The theory of probabilistic normed spaces briefly, PN-spaces is important as a generalization of ... See full document

... The 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 ... See full document

... first stability problem was raised by S.M. Ulam [35] during his talk at the University of Wisconsin in ...G 2 , ∗) be a metric group with the metric d (· , ·) ...G 2 satisfies the inequality d ... See full document

... The stability problem of functional equations originated from a question of Ulam [1] concerning the stability of group ...homomorphisms. Hyers [2] gave a first affirmative answer ... See full document

... the stability problem for functional equations is solved by direct method in which the exact solution of the functional equation is explicitly con- structed as a limit of a (Hyers) ... See full document

... 10. Ulam, SM: Problems in Modern Mathematics, chapter VI, Science ...11. Hyers, DH: On the stability of the linear functional ...the stability of the linear transformation in ... See full document

... of functional equations is as ...a functional equation must be close to an exact solution of the equation?” The first stability problem concerning group homomorphisms was raised by ... See full document

... G˘avrut¸a [10] provided a further generalization of Rassias’ theorem. During the last two decades, a number of papers and research monographs have been published on vari- ous generalizations and applications of ... See full document

... terminology Hyers-Ulam-Rassias stability originates from these historical back- ...other functional equations (see for example [4], [5], [6], [7], [10], [14], [17], [25] and the ... See full document

... On Generalized Fuzzy Normed Spaces, International Mathematical Forum, 4, 2009, ...D.H. Hyers, On the stability of the linear functional equation, ...D.H. Hyers, G. Isac, Th.M. ... See full document

... 1940, Ulam [1] proposed the general Ulam stability ...by Hyers [2] for the case of Banach ...of stability is called the Ulam-Hyers ...the Ulam-Hyers ... See full document