In the present paper, we introduce and investigate some properties of two subclasses $ Lambda_{n}( lambda , beta ) $ and $ Lambda_{n}^{+}( lambda , beta ) $;  meromorphic and starlike  functions of order $ beta $. In particular, several inclusion relations, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes.

In this paper we consider the classes of starlike functions of order α, convex functions of order α and we study the convexity and α-order convexity for some general integral operators. Several corollaries of the main results are also considered.

The goal of the present paper is to investigate some characterization for generalized Struve functions of first kind to be in the new subclasses of β uniformly starlike and β uniformly convex functions of order α. Further we point out some consequences of our main results. Mathematics subject classification: 30C45.

In this paper, we consider some relations related to the representations of starlike and convex functions, obtain sufficient conditions for functions by using theory differential subordination. Actually, generalize a result Suffridge analytic with missing coefficients then apply that generalization obtaining different methods implications or functions. Our results improve previous in literature.

In this paper, we introduce new general integral operators. New sufficient conditions for these operators to be p-valently starlike, p-valently close-to-convex, uniformly p-valent close-to-convex and strongly starlike of order γ (0 < γ ≤ 1) in the open unit disk are obtained.