We improve the Ozaki’s condition for univalence of convex functions of order a. The modified Nunokawa’s Lemma is the key in the argumentation and it may have a lot of applications in the solutions of the other problems. Some new conditions for starlikeness and strongly starlikeness of order alpha are also proved in this work. 2013 Elsevier Inc. All rights reserved.

In the present paper, using Jack’s lemma, the authors investigate the differential inequality ∣∣∣(1 − α) Ip(n,λ)f (z) zp + α Ip(n + 1, λ)f (z) Ip(n,λ)f (z) − 1 ∣∣∣ < μ, z ∈ E regarding multivalent functions defined by multiplier transfomation in the open unit disk E = {z : |z| < 1} . As consequences, sufficient conditions for univalence, starlikeness and strongly starlikeness of certain analyti...

The purpose of this paper is to prove several results in approximations through complex convolution polynomials with Jackson-type rate or with best approximation rate, having the quality of preservation of some properties in geometric function theory, like the preservation of: coefficients’ bounds, positive real part, bounded turn, close-to-convexity, starlikeness, convexity, spirallikeness, α-...

The purpose of this paper is to prove several results in approximation by complex Picard, Poisson-Cauchy, and Gauss-Weierstrass singular integrals with Jackson-type rate, having the quality of preservation of some properties in geometric function theory, like the preservation of coefficients’ bounds, positive real part, bounded turn, starlikeness, and convexity. Also, some sufficient conditions...

We consider certain properties of f(z)f ′′(z)/f ′2(z) as a sufficient condition for starlikeness.

By using the method of differential subordination, we obtain some sufficient conditions for strongly p-valent starlikeness.

This paper deals with local convexity properties of the j-metric. We consider convexity and starlikeness of the j-metric balls in convex, starlike and general subdomains of R.

Abstract. The author here wish to further study the new concept of analytic and univalent functions normalized with f(ω) and f ′(ω) − 1 = 0 introduced by Kanas and Ronning in 1999 which was later also investigated in 2005 by Acu and Owa. The author in this paper obtain coefficient estimates, distortion theorems, convex linear combinations, and radii of ω-closeto-convex, ω − starlikeness and ω −...