On two functional equations and their solutions

Abstract

The present work aims to determine the solution f : R 2

On functional equations of the multiplicative type

“…for all x, y, u, v ∈ R. Houston and Sahoo [8] proved the following theorem concerning the above functional equation. where M : R → R is a multiplicative function.…”

“…This functional equation was solved in [8] and also in [10]. A generalization of the functional equation (1.17) is…”

“…for all x, y, u, v ∈ R. The general solution of (1.22) was determined in [8]. To find the general solution of a more general equation than (1.22), the solution of the following functional equation was needed:…”

Conditional functional equations on restricted domains of measure zero

“…In the present paper, as a modified version of the equations in Chung-Chang [9], Chung-Sahoo [11], Houston-Sahoo [14,24] and Jung-Bae [18] we consider the functional inequalities…”

Stability of Exponential Functional Equations with Involutions

“…for all ∈ (see Albert and Baker [3]). In [4][5][6], some functional equations arising from number theory or product of matrices are introduced. The equations therein can be reduced to the functional equations with involution : → :…”