On a subclass of analytic functions defined by Ruscheweyh derivative and multiplier transformations

Let A (p, n) = {f is an element of H(U) : f(z) = z(p) + Sigma(infinity)(j=p+n) a(j)z(j), z is an element of U}, with A(1, 1) = A. We consider in this paper the operator RI gamma (m, lambda, l) : A -> A, defined by RI gamma (m, lambda, l)f(z) := (1 - gamma) R-m f (z) + gamma I (m, lambda, l)f(z) where I(m, lambda, l)f(z) = z + Sigma(infinity)(j=2) [1+lambda(j-1)+1/l+1](m) a(j)z(j) and (m + 1)Rm+1 f (z) = z(R-m f (z))' + mR(m) f (z), m is an element of N-0,N- N-0 = N U {0}, lambda is an element of R, lambda >= 0, l >= 0 is the Ruscheweyh operator. By making use of the above mentioned differential operator, a new subclass of univalent functions in the open unit disc is introduced. The new subclass is denoted by RI gamma (m, mu, alpha, lambda, l). Parallel results, for some related classes including the class of starlike and convex functions respectively, are also obtained.