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).

ULAM STABILITY OF GENERALIZED RECIPROCAL ...

e-mail: shcravi@yahoo.co.in. 2 Department of Mathematics,. C.Abdul Hakeem College of Engg. and Tech.,. Melvisharam - 632 509,TamilNadu, India. e-mail: bvssree@yahoo.co.in. Abstract. In this paper, we introduce the Generalized Reciprocal Functional. Equation (or GRF equation) in several variables of the form f. ( m.
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