[PDF] Top 20 On the Probabilistic Stability of the 2-variable $k$-AC-mixed Type Functional Equation

... the stability of the linear transformation in Banach spaces, ...Japan, 2 (1950), ...Ulam-Hyers stability of a 2-variable AC-mixed type functional ... See full document

... Hyers 2 in the case of Banach space. Thereafter, we call that type the Hyers-Ulam ...various functional equations and their Hyers-Ulam stability ...Hyers-Ulam stability is a classical ... See full document

... first stability problem concerning group ...This stability is also investigates by Park ...other type fuzzy norms and some properties of fuzzy normed linear spaces ...versions stability ... See full document

... an additive functional equations. Also, we obtain its general solution from the stability results. Copyright q 2008 Kil-Woung Jun et al. This is an open access article distributed under the Creative Commons ... See full document

... of probabilistic metric spaces. Since then, the theory of probabilistic metric spaces has been developed by many authors in many directions; see [6], [7] and the references ...a probabilistic metric ... See full document

... The stability of mixed type functional equations have been extensively investigated by a number of math- ematicians in referenes (see [3–5, 14–22, 28–31, 33–38, 43, 48, ... See full document

... 1940. 2 D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and Their Applications, 34, Birkh¨auser, Boston, ... See full document

... Over the last seven decades, the above problem was tackled by numerous authors and its solutions via various forms of functional equations including mixed type additive and cubic functional ... See full document

... = k 2 f (x + y) + k 2 f (x − y) + 2(1 − k 2 )f (x) (1:5) in quasi-Banach spaces, where k is nonzero integer numbers with k ≠ ± ...bx 2 + cx 3 is a ... See full document

... the stability of the linear functional ...the stability of the linear mapping in Banach ...S: Functional Equations and Inequalities in Several ...Hyers-Ulam-Rassias stability of ... See full document

... In 1984, Katsaras [18] defined a fuzzy norm on a linear space to construct a fuzzy structure on the space. Since then, some mathematicians have introduced several types of fuzzy norm in different points of view. In ... See full document

... of stability for functional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the ...Hyers 2 gave a first affirmative answer ... See full document

... F ( R ) → S ( R ), S ( R ) → F ( R ). (2 : 3) Taking the relations (2.3) into account, it suffices to consider the space F ( R ) . In order to solve the general solution and the stability problem of (1.2) ... See full document

... of stability problems of functional equations, the stability phenomenon that was proved by Rassias is called the gen- eralized Ulam-Rassias stability or Hyers-Ulam-Rassias stability ... See full document

... functional equation 1.5, which is called a quartic functional equation see also ...Hyers-Ulam stability for a mixed type of quartic and quadratic functional ... See full document

... resulting equation by θ n (resp.γ n ) and replace n by −m in the resulting equation, then we obtain a equation with m in place of n, where m ∈ {0, −1, −2, ...and k ∈ N ... See full document

... tional equation (1.1) is said to be a quadratic mapping. A Hyers-Ulam stability pro- blem for the quadratic functional equation was proved by Skof [5] for mappings f : X → Y , where X is a ... See full document

... for all x, y ∈ X. In this case, a quasi-Banach space is called a p–Banach space. By the Aoki-Rolewicz Theorem [14], each quasi-norm is equivalent to some p– norm (see also [2]). Since it is much easier to work ... See full document

... an equation is called a quadratic functional ...quadratic functional equation (.). A Hyers-Ulam stability problem for the quadratic functional equation ... See full document

... functional equation. In particular, every solution of the quadratic functional equation is said to be quadratic ...of stability theory of functional equations for the proof of ... See full document