T. V. Sudharsan

S.I.V.E.T College of Arts & Science | SIVET · Department of Mathematics

The present extensive study is focused to find estimates for the upper bounds of the Toeplitz determinants. The logarithmic coefficients of univalent functions play an important role in different estimates in the theory of univalent functions, and in the this paper we derive the estimates of Toeplitz determinants and Toeplitz determinants of the lo...

In this paper we introduce the subclass T S λ p (µ, α, β, δ), 0 ≤ µ < 1, 0 ≤ α < 1, λ, β ≥ 0 of analytic functions with negative coefficients. This class is motivated by the study of Sudharsan et al. (2010). We obtain a coefficient characterization, growth and distortion theorems, closure theorem and a convolution result for functions in this class...

The main aim of the present paper is to obtain an upper bound on the third Hankel determinant for the new class of univalent functions defined in the unit disk U using an integral operator.

In this paper, we define the [Formula: see text]th Vandermonde determinant and determine the coefficient bounds for the second- and third-order Vandermonde determinant for a Sakaguchi type function [Formula: see text] and [Formula: see text] which map open unit disc onto the region bounded by Limaçon [Formula: see text] Sharp upper bounds are obtai...

The main object of this article is to define a new class of analytic functions using q - Sãlãgean differential operator involving complex order. We obtain coefficient estimates and other useful properties for this new class.

Let A be the class of analytic functions f(z) in the unit disc ∆ = {z ∈ C: |z| < 1} with the Taylor series expansion about the origin given by f(z) = z + ∑∞n=2 anzⁿ, z ∈ ∆. The focus of this paper is on deriving upper bounds for the third order Hankel determinant H3(1) for two new subclasses of A.

In this paper, by applying the Hohlov linear operator, connections between the class SD(α) , α≥0 , and two subclasses of the class A of normalized analytic functions are established. Also an integral operator related to hypergeometric function is considered.

We introduce two new subclasses of the function class Σ of biunivalent functions in the open disc defined by convolution. Estimates on the coefficients a2 and a3 for the two subclasses are obtained. Moreover, we verify Brannan and Clunie’s conjecture a2≤2 for our subclasses.

This paper focuses on attaining the upper bounds on $H_3(1)$ for a class $C_\alpha^\beta(0 \leq \beta<1, \alpha \geq 0)$ in the unit $\operatorname{disk} \Delta=\{z \in \mathbb{C}:|z|<1\}$.

The main object of this paper is to obtain inclusion relations between certain classes of normalized analytic functions, which are introduced here by means of Hohlov operator. Special cases of these inclusion relations are shown to yield known results.

New classes of meromorphic functions with varying argument of coefficients defined by means of the Hadamard product or convolution are introduced and investigated. We obtain coefficient estimates, distortion properties and the radii of starlikeness and convexity, and partial sums for the classes of meromorphic functions with varying argument of coe...

In this paper we introduce the classes T S λ p (α, β) and T V λ (α, β), α ∈ [−1, 1), λ ≥ 0, β ≥ 0 of analytic functions with negative coefficients. The classes are motivated by the study of Acu and Owa (2006). We obtain a coefficient charac-terization, growth and distortion theorems and a convolution result for functions in these classes. 2000 Math...

A new subclass of Salagean-type harmonic univalent function is in-troduced. Coefficient conditions, extreme points, distortion bounds, convolution conditions, convex combinations and radii of convexity for this subclass are ob-tained.

A class of complex-valued harmonic meromorphic functions of the form f (z) = h(z)+g(z), |z| > 1, is introduced. It is shown that the functions in this class are orientation preserving and univalent outside the unit disk. Necessary and Sufficient coefficient conditions are obtained for functions in this class, which are also shown to be necessary wh...

A class of Salagean-type harmonic univalent functions is defined and investigated. Coefficient conditions, extreme points, distortion bounds, convex combination and radii of convexity for this class, are obtained.

Two new subclasses of uniformly convex and uniformly close-to-convex functions are introduced. We obtain inclusion relationships and coefficient bounds for these classes.

We give coefficient characterizations for analytic functions with negative coefficients to be in subclasses of uniformly starlike and uniformly convex families. This leads to extremal properties and neighborhood criteria.

A class S*s(α, ß) of functions f, regular and univalent in D = {z : \z\ < 1} given by f(z) = z + Σn=2∞ anzn and satisfying the condition Formula Presented z ∈ D, 0 ≤ α ≤ 1, 0 < ß ≤ 1 is introduced and studied. An analogous class S*c(α, ß) is also examined.

A coefficient inequality for a new class of harmonic multivalent functions is derived and is found to be a sufficient condition for harmonic multivalent functions to belong to this class. This condition is shown to be also necessary for a subclass of the new class introduced here. Certain other properties of the subclass are also obtained.