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In this paper, we introduce the concept of quasi-convex functions by considering a subclass [Formula: see text] of normalized analytic functions in the unit disk [Formula: see text] for some convex function [Formula: see text] with fixed second coefficient of order [Formula: see text], such that [Formula: see text] We obtain results on growth and distortion theorems and radius of convexity.

In the present paper, we introduce and investigate some new subclasses of α-starlike and α -close to convex functions with respect to symmetric conjugate points. Inclusion relationships, integral representations and some interesting convolution properties for these functions are obtained.

In the present paper, by introducing a new subclass of multivalent functions with respect to - symmetric points, we have obtained the integral representations and conditions for starlikeness using differential subordination.

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