In this paper,we define a class of analytic functions F-(beta,lambda()) (H, alpha, delta, mu), satisfying the following subordinate condition associated with Chebyshev polynomials {alpha[zG' (z)/G (z)](delta) + (1 - alpha) [zG' (z)/G (z)](mu) [1 + zG '' (z)/G' (z)](1-mu)} < H (z, t), where G(z) = lambda beta z(2)f '' (z) + (lambda - beta) zf' (z) + (1 - lambda + beta) f (z) , 0