DEMONSTRATE MATHEMATICA Vol. XXX No 2 1997 Vijay Gupta, D. Kumar RATE OF CONVERGENCE OF MODIFIED BASKAKOV OPERATORS 1. Introduction Modified Baskakov operator [4] is defined as ? OO oo ^¡¡f! £„(/,*) = ( n - J p n , k (t)f(t)dt, x G [0, oo) k=0 0 where p n , k (x) = + *)— Gupta and Agrawal [2] estimated the rate of convergence of modified Szasz-Mirakyan operators for functions of bounded variation. Sahai and Prasad [3] gave correct and improved estimate for modified Szasz opera- tors for functions of bounded variation. In the present paper, we study the analogous problem for modified Baskakov operators B n (f,x) for functions of bounded variation, using some results of probability theory considering the functions bounded on [0,oo). 2. Auxiliary results To prove the main theorem, we shall need the following results: LEMMA 1 [5]. //{£,}, i — 1,2,... are independent random variables with same geometric distribution P{di = k}= f-^-) *>0; ¿ = 0,1,... \ 1 + X / 1 T £ then E(tt) = x, p 2 = E(£i - E(fc)) 2 = x(l + x) and Vn = is a random variable with distribution 1991 Mathematics Subject Classification: 41A30, 41A36.