Sukhjit Singh - Academia.edu (original) (raw)

Papers by Sukhjit Singh

Proceedings of The American Mathematical Society, 1989

Let R denote the class of functions f(z) = z + aiz2 H-that are analytic in the unit disc E = {z: ... more Let R denote the class of functions f(z) = z + aiz2 H-that are analytic in the unit disc E = {z: \z\ < 1} and satisfy the condition Re(/'(z) + zf"(z)) > 0 > z e E. It is known that R is a subclass of S¡, the class of univalent starlike functions in E . In the present paper, among other things, we prove (i) for every n > 1 , the nth partial sum of / € R, sn(z,f), is univalent in E , (ii) R is closed with respect to Hadamard convolution, and (iii) the Hadamard convolution of any two members of R is a convex function in E.


In this paper, we obtain some sufficient conditions for a normalized analytic function to be φ-li... more In this paper, we obtain some sufficient conditions for a normalized analytic function to be φ-like and starlike of order α.

Let α, β, γ and δ be complex numbers such that β, δ = 0.

International Journal of Mathematics and Mathematical Sciences, 2000

Let K(α), 0 ≤ α < 1, denote the class of functions g(z) = z + ∞ n=2 a n z n which are regular and... more Let K(α), 0 ≤ α < 1, denote the class of functions g(z) = z + ∞ n=2 a n z n which are regular and univalently convex of order α in the unit disc U. Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U, f (0) = 0, and f (z)

International Journal of Mathematics and Mathematical Sciences, 2000

We prove a subordination relation for a subclass of the class of λ-spirallike functions.

Applied Mathematics Letters, 2006

In the present paper by using the method of differential subordination we aim to prove some class... more In the present paper by using the method of differential subordination we aim to prove some classical results in univalent function theory. In particular we give some new sufficient condition for an analytic function to be starlike and convex in the unit disc U . Also by applying Ruscheweyh derivative we investigate some argument properties of some subclasses of univalent functions.

Bulletin of The Belgian Mathematical Society-simon Stevin, 2005

Denote by A ′ , the class of functions f , analytic in E which satisfy f (0) = 1. Let α > 0, β ∈ ... more Denote by A ′ , the class of functions f , analytic in E which satisfy f (0) = 1. Let α > 0, β ∈ (0, 1] be real numbers and let γ, Reγ > 0, be a complex number. For p, q ∈ A ′ , the authors study the differential subordination of the form

In the present paper, the authors investigate starlikeness and convexity of a class of multivalen... more In the present paper, the authors investigate starlikeness and convexity of a class of multivalent functions defined by multiplier transfomation. As a consequence, a number of sufficient conditions for starlikeness and convexity of analytic functions are also obtained.

Let p and q be analytic functions in the unit disc E = {z : |z| < 1}, with p(0) = q(0) = 1. Assum... more Let p and q be analytic functions in the unit disc E = {z : |z| < 1}, with p(0) = q(0) = 1. Assume that α and δ are real numbers such that 0 < δ ≤ 1, α + δ ≥ 0. Let β and γ be complex numbers with β = 0. In the present paper, we investigate the differential subordination

Integral Transforms and Special Functions, 2005

Let A be the class of functions f , analytic in E = {z : |z| < 1} and normalized by the condition... more Let A be the class of functions f , analytic in E = {z : |z| < 1} and normalized by the conditions f (0) = f (0)−1 = 0. In the present note, we prove that f ∈ A, satisfying the differential inequality

International Journal of Mathematics and Mathematical Sciences, 2003

Let K denote the class of functions g(z) = z + a 2 z 2 + ··· which are regular and univalently co... more Let K denote the class of functions g(z) = z + a 2 z 2 + ··· which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is

Proceedings of The American Mathematical Society, 1989

Let R denote the class of functions f(z) = z + aiz2 H-that are analytic in the unit disc E = {z: ... more Let R denote the class of functions f(z) = z + aiz2 H-that are analytic in the unit disc E = {z: \z\ < 1} and satisfy the condition Re(/'(z) + zf"(z)) > 0 > z e E. It is known that R is a subclass of S¡, the class of univalent starlike functions in E . In the present paper, among other things, we prove (i) for every n > 1 , the nth partial sum of / € R, sn(z,f), is univalent in E , (ii) R is closed with respect to Hadamard convolution, and (iii) the Hadamard convolution of any two members of R is a convex function in E.


In this paper, we obtain some sufficient conditions for a normalized analytic function to be φ-li... more In this paper, we obtain some sufficient conditions for a normalized analytic function to be φ-like and starlike of order α.

Let α, β, γ and δ be complex numbers such that β, δ = 0.

International Journal of Mathematics and Mathematical Sciences, 2000

Let K(α), 0 ≤ α < 1, denote the class of functions g(z) = z + ∞ n=2 a n z n which are regular and... more Let K(α), 0 ≤ α < 1, denote the class of functions g(z) = z + ∞ n=2 a n z n which are regular and univalently convex of order α in the unit disc U. Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U, f (0) = 0, and f (z)

International Journal of Mathematics and Mathematical Sciences, 2000

We prove a subordination relation for a subclass of the class of λ-spirallike functions.

Applied Mathematics Letters, 2006

In the present paper by using the method of differential subordination we aim to prove some class... more In the present paper by using the method of differential subordination we aim to prove some classical results in univalent function theory. In particular we give some new sufficient condition for an analytic function to be starlike and convex in the unit disc U . Also by applying Ruscheweyh derivative we investigate some argument properties of some subclasses of univalent functions.

Bulletin of The Belgian Mathematical Society-simon Stevin, 2005

Denote by A ′ , the class of functions f , analytic in E which satisfy f (0) = 1. Let α > 0, β ∈ ... more Denote by A ′ , the class of functions f , analytic in E which satisfy f (0) = 1. Let α > 0, β ∈ (0, 1] be real numbers and let γ, Reγ > 0, be a complex number. For p, q ∈ A ′ , the authors study the differential subordination of the form

In the present paper, the authors investigate starlikeness and convexity of a class of multivalen... more In the present paper, the authors investigate starlikeness and convexity of a class of multivalent functions defined by multiplier transfomation. As a consequence, a number of sufficient conditions for starlikeness and convexity of analytic functions are also obtained.

Let p and q be analytic functions in the unit disc E = {z : |z| < 1}, with p(0) = q(0) = 1. Assum... more Let p and q be analytic functions in the unit disc E = {z : |z| < 1}, with p(0) = q(0) = 1. Assume that α and δ are real numbers such that 0 < δ ≤ 1, α + δ ≥ 0. Let β and γ be complex numbers with β = 0. In the present paper, we investigate the differential subordination

Integral Transforms and Special Functions, 2005

Let A be the class of functions f , analytic in E = {z : |z| < 1} and normalized by the condition... more Let A be the class of functions f , analytic in E = {z : |z| < 1} and normalized by the conditions f (0) = f (0)−1 = 0. In the present note, we prove that f ∈ A, satisfying the differential inequality

International Journal of Mathematics and Mathematical Sciences, 2003

Let K denote the class of functions g(z) = z + a 2 z 2 + ··· which are regular and univalently co... more Let K denote the class of functions g(z) = z + a 2 z 2 + ··· which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is