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In this paper, by using the theory of differential subordination, we will generalize Jack’s lemma for functions with fixed initial coefficient. Then extensions of the well-known open-door lemma for analytic and meromorphic functions with fixed initial coefficient are given. Also we consider some applications of the extension of Jack’s lemma. [ABSTRACT FROM AUTHOR]

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

The conditions on A, B, β and γ are obtained for an analytic function p defined on the open unit disc D and normalized by p(0) = 1 to be subordinate to (1 + Az)/(1 + Bz), −1 ≤ B < A ≤ 1 when p(z) + zp' (z)/(βp(z) + γ) is subordinate to ez . The conditions on these parameters are derived for the function p to be subordinate to √ 1 + z or ez when p(z) + zp0 (z)/(βp(z) + γ) is subordinate to (1 + Az)/(1 + Bz). The conditions on β and γ are determined for the function p to be subordinate to ez when p(z)+zp'(z)/(βp(z)+γ) is subordinate to √ 1 + z. Related result for the function p(z) + zp' (z)/(βp(z) + γ) to be in the parabolic region bounded by the Re w = |w − 1| is investigated. Sufficient conditions for the Bernardi’s integral operator to belong to the various subclasses of starlike functions are obtained as applications. [ABSTRACT FROM AUTHOR]

The notions of strong differential subordination and superordination have been studied recently by many authors. In the present paper, using these concepts, we obtain some preserving properties of certain nonlinear integral operator defined on the space of normalized analytic functions in 픻x픻. The sandwich-type theorems and consequences of the main results are also considered. [ABSTRACT FROM AUTHOR]

In this paper we investigate the radii problem for harmonic functions with a fixed coefficient and determine the radii of univalence, stable starlikness, stable convexity, fully starlikness and fully convexity of order α for these type of functions. All results are sharp. Also these results generalize and improve some results in the literature. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to investigate starlikeness of certain integral operators, which are defined here by means of iterative in the open disk DR = {z ϵ C : |z| < R} with R ⩾ 1. Also we prove that these result are best possible. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to derive some results for multivalent analytic functions defined by a linear operators. As a special case of these results, we obtain several sufficient conditions for close-to-convexity and starlikeness of certain analytic functions. [ABSTRACT FROM AUTHOR]

In the present paper we introduce the subclass Saclambda (p,A,B) of analytic functions and then we investigate some interesting properties of functions belonging to this subclass. Our results generalize many results known in the literature and especially generalize some of the results obtained by Ling and Liu [5]. [ABSTRACT FROM AUTHOR]

Using the fixed point method, we prove the Hyers-Ulam stability of ternary homomorphisms and ternary derivations in fuzzy ternary Banach algebras associated to the following additive functional equation ... for a fixed integer n with n ≥ 2. [ABSTRACT FROM AUTHOR]