Some Properties of a Class of Analytic Functions Involving a New Generalized Differential Operator

In the present paper, we introduce a new generalized differential operator D-mu,lambda,sigma(m) (alpha, beta) defined on the open unit disc U = {z is an element of C : vertical bar z vertical bar < 1}. A novel subclass Omega(m)*(delta, lambda, alpha, beta, b) by means of the operator D-mu,lambda,sigma(m) (alpha, beta) is also introduced. Coefficient estimates, growth and distortion theorems, closure theorems, and class preserving integral operators for functions in the class Omega(m)*(delta, lambda, alpha, beta, b) are discussed. Furthermore, sufficient conditions for close-to-convexity, starlikeness, and convexity for functions in the class Omega(m)*(delta, lambda, alpha, beta, b) are obtained.