ASYMPTOTIC BEHAVIORS OF ALTERNATIVE JENSEN FUNCTIONAL EQUATIONS-REVISITED

Asymptotic behavior of alternative Jensen and Jensen type functional equations

In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982–2005 we established the Hyers–Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1998 S.-M. Jung and in 2002–2005 the authors of this paper investigated the Hyers–Ulam stability of additive ...

Stability of Jensen-Type Functional Equations on Restricted Domains in a Group and Their Asymptotic Behaviors

Asymptotic aspect of Jensen and Jensen type functional equations in multi-normed spaces

In this paper, we investigate the Hyers-Ulam stability of additive functional equations of two forms: of “Jensen” and “Jensen type” in the framework of multi-normed spaces. We therefore provide a link between multi-normed spaces and functional equations. More precisely, we establish the Hyers-Ulam stability of functional equations of these types for mappings from Abelian groups into multi-norme...

Stability of a Jensen Type Logarithmic Functional Equation on Restricted Domains and Its Asymptotic Behaviors

Let R be the set of positive real numbers, B a Banach space, f : R → B, and > 0, p, q, P,Q ∈ R with pqPQ/ 0. We prove the Hyers-Ulam stability of the Jensen type logarithmic functional inequality ‖f xy − Pf x − Qf y ‖ ≤ in restricted domains of the form { x, y : x > 0, y > 0, xy ≥ d} for fixed k, s ∈ R with k / 0 or s / 0 and d > 0. As consequences of the results we obtain asymptotic behaviors ...

Suffix Trees Revisited: (Un)Expected Asymptotic Behaviors

Suffix trees find several applications in computer sciences and telecommunications, most notably in algorithms on strings, data compressions and codes. Despite this, very little is known about their typical behavior. We consider in a probabilistic framework a family of suffix trees further called b-suffix trees built from the first n suffixes of a random word. In this family a noncompact suffix...