Let Ap(p ∈ N) be the class of functions f(z) = z + ∑∞ m=1 ap+mz p+m which are analytic in the unit disk. By virtue of the Ruscheweyh derivatives we introduce the new subclasses Cp(n, α, β, λ, μ) of Ap. Subordination relations, inclusion relations, convolution properties and a sharp coefficient estimate are obtained. We also give a sufficient condition for a function to be in Cp(n, α, β, λ, μ).

in this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. we give some sufficient conditions for functions belonging to this class.

This paper introduces and studies a new class of analytic p-valent functions in the open symmetric unit disc involving Sălăgean-type q-difference operator. Furthermore, we present several interesting subordination results, coefficient inequalities, fractional q-calculus applications, distortion theorems.

In this paper, subclasses of the function class ∑ analytic and bi-univalent functions associated with operator L_q^(k, λ) are introduced defined in open unit disk △ by applying quasi-subordination. We obtain some results about corresponding bound estimations coefficients a_(2 ) a_(3 ).