On certain subclass of normalized analytic function associated with Rusal differential operator

Abstract

In this article the author discusses the two subclasses namely $\check{K}_p\left(A_\lambda^n ; \gamma, \mu, m, \beta\right)$ and $K_p\left(A_\lambda^m ; \gamma, \mu, m, \beta\right)$ of normalized analytic functions. With convex combination of Ruschwey and Al-Oboudi differential operator we derived Rusal differential operator. Two new subclasses $\check{K}_p\left(A_\lambda^n ; \gamma, \mu, m, \beta\right)$ and $K_p\left(A_\lambda^n ; \gamma, \mu, m, \beta\right)$ are studied with help of Rusal differential operator.Growththeorem, Closure theorem, Integral mean inequality, extreme point theorem, coefficient inequality, convolution and distortion theorem for given class are examined.