Stability of mixed-type trigonometric and quadrstic functional equations

Abstract

The first part of the thesis proves the stability of a generalized trigonometric functional equation F G H K over the domain of an abelian group and the range of the complex field. Several related results extending a number of previously known ones, such as the ones dealing with the sine functional equation, the d’Alembert functional equation and Wilson functional equation, are derived as direct consequences and applications to operators in Banach algebra are derived. The second part of the thesis first determines differentiable solution functions of a mixed-type trigonometric and quadratic functional equation of the form F G H K L M over the domain of the real number field and the range of the complex field. Then the stability of this latter functional equation over the domain of an abelian group and the range of the compiex field, is proved.