On certain general integral operators of analytic functions

In this paper, we obtain new sufficient conditions for the operators $F_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)$ and $G_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)$ to be univalent in the open unit disc $\mathcal{U}$, where the functions $f_1, f_2,..., f_n$ belong to the classes $S^*(a, b)$ and $\mathcal{K}(a, b)$. The order of convexity for the operators $F_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)$ and $G_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)$ is also determined. Furthermore, and for $\beta= 1$, we obtain sufficient conditions for the operators $F_n(z)$ and $G_n(z)$ to be in the class $\mathcal{K}(a, b)$. Several corollaries and consequences of the main results are also considered

Salagean-type harmonic univalent functions with fixed finitely many coefficients

In the present paper, authors introduce and study a new class of Salagean-type harmonic univalent functions that have fixed finitely many coefficients. We obtain coefficient conditions, extreme points, convolution condition, convex combinations for the above class of harmonic univalent functions

CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING COMPLEX ORDER

Abstract In the present investigation, we consider an unified class of functions of complex order. Necessary and sufficient condition for functions to be in this class is obtained. The results obtained in this paper generalizes the results obtained by Srivastava and Lashin [10], and Ravichandran et al

New sufficient conditions for univalence

Abstract The object of the present paper is to obtain new sufficient conditions on f (z) which lead to some subclasses of univalent functions defined in the open unit disk

General Integral Operator of Analytic Functions Involving Functions with Positive Real Part

Let be the integral operator defined by where each of the functions and are, respectively, analytic functions and functions with positive real part defined in the open unit disk for all . The object of this paper is to obtain several univalence conditions for this integral operator. Our main results contain some interesting corollaries as special cases