Functional Equations and Inequalities

Functional Equations andInequalities provides an extensive studyofsome of the most important topics of current interest in functional equations and inequalities. Subjects dealt with include: a Pythagorean functional equation, a functional definition oftrigonometric functions, the functional equation ofthe square root spiral, a conditional Cauchy functional equation, an iterative functional equation, the Hille-type functional equation, the polynomial-like iterative functional equation, distribution ofzeros and inequalities for zeros of algebraic polynomials, a qualitative study ofLobachevsky's complex functional equation, functional inequalities in special classesoffunctions, replicativity and function spaces, normal distributions, some difference equations, finite sums decompositions of functions, harmonic functions, set-valued quasiconvex functions, the problem of expressibility in some extensions of free groups, Aleksandrov problem and mappings which preserve distances, Ulam's problem, stability of some functional equation for generalized trigonometric functions, Hyers-Ulam stability of Hosszil's equation, superstability of a functional equation, and some demand functions in a duopoly market with advertising. It is a pleasureto express my deepest appreciationto all the mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staffofKluwer Academic Publishers. June 2000 Themistocles M. Rassias xi ON THE STABILITY OF A FUNCTIONAL EQUATION FOR GENERALIZED TRIGONOMETRIC FUNCTIONS ROMAN BADORA lnstytut Matematyki, Uniwersytet Sli;ski, ul. Bankowa 14, PL-40-007 Katowice, Poland, e-mail: robadora@gate. math. us. edu. pl Abstract. In the present paper the stability result concerning a functional equation for generalized trigonometric functions is presented. Z.