Let B be the class of analytic functions f in the unit disk D := {z is an element of C : vertical bar z vertical bar |g (z)| with 0 <= alpha < 1, g' (0) = 0, z. D} be the subclass of close-to-convex harmoni...
详细信息
Let B be the class of analytic functions f in the unit disk D := {z is an element of C : vertical bar z vertical bar < 1} such that vertical bar f (z) vertical bar< 1 for all z. D. If f. B is of the form f (z) = Sigma(infinity)(n=0) a(n) z(n), then vertical bar Sigma(N)(n=0) an zn vertical bar < 1 holds for |z| < 1/2 and the radius 1/2 is best possible for the class B. This inequality is called the Rogosinski inequality and the corresponding radius is called the Rogosinski radius. Let H be the class of harmonic functions f = h + (g) over bar in the unit disk D, where h and g are analytic in D. Let P-H(0) (a) = {f = h + (g) over bar is an element of H : Re(h' (z) - alpha) > |g (z)| with 0 <= alpha < 1, g' (0) = 0, z. D} be the subclass of close-to-convex harmonic mappings. In this paper, in view of the Euclidean distance, we obtain the sharp Bohr-Rogosinski radius in terms of area measure Sr, Jacobian J f ( z) of the functions in the class P0H (a).
In this paper, we introduce several new subclasses of the analytic functions defined in the open unit disc U that are associated with the Pascal operator. Furthermore, inclusion relations and integral preserving prope...
详细信息
In this paper, we introduce several new subclasses of the analytic functions defined in the open unit disc U that are associated with the Pascal operator. Furthermore, inclusion relations and integral preserving properties of these subclasses are derived.
The main focus of the present paper is to establish sufficient conditions for the parameters of the normalized form of the generalized Le Roy-type Mittag-Leffler function have certain geometric properties like close-t...
详细信息
The main focus of the present paper is to establish sufficient conditions for the parameters of the normalized form of the generalized Le Roy-type Mittag-Leffler function have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disc. The results are new and their usefulness is depicted by deducing several interesting corollaries. The results improve several results available in the literature for the Mittag-Leffler function.
In this paper, the products of modified Bessel functions of the first kind are considered. Our main aim is to provide various conditions so that these products have certain geometric properties such as starlikeness, c...
详细信息
In this paper, the products of modified Bessel functions of the first kind are considered. Our main aim is to provide various conditions so that these products have certain geometric properties such as starlikeness, convexity, and close to convexity (univalency) with respect to certain functions in the unit disk. Subordinating factor sequences for these products are also obtained. Interesting consequences are provided. The results obtained are new in the literature.
This manuscript investigates the classical problem of determining conditions on the parameters alpha, beta is an element of C for which the integral transform C-alpha beta[phi](z) := integral(z)(0) (phi(zeta)/zeta(1 -...
详细信息
This manuscript investigates the classical problem of determining conditions on the parameters alpha, beta is an element of C for which the integral transform C-alpha beta[phi](z) := integral(z)(0) (phi(zeta)/zeta(1 - zeta)(beta))(alpha) d zeta is also univalent in the unit disk, where phi is a normalized univalent function. Additionally, whenever phi belongs to some subclasses of the class of univalent functions, the univalence features of the harmonic mappings corresponding to C-alpha beta[phi] and its rotations are derived. As applications to our primary findings, a few non-trivial univalent harmonic mappings are also provided. The primary tools employed in this manuscript are Becker's univalence criteria and the shear construction developed by Clunie and Sheil-Small. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox-Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starl...
详细信息
The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox-Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disc. In particular, we study some geometric properties for some class of functions related to the generalized hypergeometric functions.
We consider the convolution of right half-plane harmonic mappings in the unit diskD:={z is an element of C:vertical bar z vertical bar<1} with respective dilatations e(i alpha)(z+a)/(1+az) and -z, where-1<a<1...
详细信息
We consider the convolution of right half-plane harmonic mappings in the unit diskD:={z is an element of C:vertical bar z vertical bar<1} with respective dilatations e(i alpha)(z+a)/(1+az) and -z, where-1convex in the horizontal direction under certain condition.
In this paper two subclasses B sigma (alpha, lambda) and B sigma(beta, lambda) are studied and a new estimation for the initial coefficients |a2| and |a3| in these subclasses are found.
In this paper two subclasses B sigma (alpha, lambda) and B sigma(beta, lambda) are studied and a new estimation for the initial coefficients |a2| and |a3| in these subclasses are found.
Let H be the class of harmonic functions f = h + (g) over bar in the unit disk D := {z is an element of C : |z| |g'(z)| with 0 <= alpha < 1, g' (0) = 0, z is an element of D} be the class of close-tocon...
详细信息
Let H be the class of harmonic functions f = h + (g) over bar in the unit disk D := {z is an element of C : |z| < 1}, where h and g are analytic in D. Let P-H(0)(alpha) = {f = h + (g) over bar is an element of H : Re (h'(z) - alpha) > |g'(z)| with 0 <= alpha < 1, g' (0) = 0, z is an element of D} be the class of close-toconvex mappings defined by Li and Ponnusamy (Nonlinear Anal 89:276-283, 2013). In this paper, we obtain the sharp Bohr-Rogosinski radius, improved Bohr radius and refined Bohr radius for the class P-H(0) (alpha).
暂无评论