. 2 Department of Mathematics,. C.Abdul Hakeem College of Engg. and Tech.,. Melvisharam - 632
ULAM STABILITY OF GENERALIZED RECIPROCAL FUNCTIONAL EQUATION IN SEVERAL VARIABLES K. RAVI1 AND B.V. SENTHIL KUMAR2
1
Department of Mathematics, Sacred Heart College, Tirupattur-635 601, TamilNadu, India. e-mail:
[email protected] 2
Department of Mathematics,
C.Abdul Hakeem College of Engg. and Tech., Melvisharam - 632 509,TamilNadu, India. e-mail:
[email protected] Abstract. In this paper, we introduce the Generalized Reciprocal Functional Equation (or GRF equation) in several variables of the form
f
m X i=1
! αi xi
h =P m i=1
Qm f (xi ) i=1 Q
αi
m j=1,j6=i
i f (xj )
(0.1)
for arbitrary but fixed real numbers (α1 , α2 , . . . , αm ) 6= (0, 0, . . . , 0), so that Pm 0 < α = α1 + α2 + · · · + αm = i=1 αi 6= 1 and f : X → Y with X and Y are the sets of non-zero real numbers. Besides, we solve the pertinent Ulam stability problem for this GRF equation (0.1). We discuss the Hyers-Ulam stability, Generalized Ulam (or Ulam-Gavruta-Rassias) stability, the extended Ulam (or Extended Rassias) stability and Refined Ulam (or Refined Rassias) stability problems for the equation (0.1).
