On Stability and Superstability of Some Generalized Cauchy Functional Equations

Abstract

In this thesis, we study some importants facts on Cauchy functional equations and we study the stability and superstability of some generalized Cauchy functional equations. We study the Hyers-Ulam, Th. M. Rassias and Gavruta Stability of a generalized Cauchy linear functional equation such that the Cauchy difference of a generalized Cauchy linear functional equation is bounded or unbounded. After this, we study the Hyers-Ulam Stability of some Cauchy functional equations such that the Cauchy difference of a Cauchy functional equations is bounded. Also we study the superstability of some generalized Cauchy functional equations such that the Cauchy difference of a generalized Cauchy functional equations is bounded.