Abstract:

The purpose of this present paper is to derive some subordination and superordination results for certain normalized analytic functions in the open unit disk, acted upon by Dziok-Srivastava operator. Relevant connections of the results, which are presented in this paper, with various known results are also considered.

Paper's Title:

Coefficient Bounds for Sakaguchi Kind of Functions Associated with Sine Function

Author(s):

Serap Bulut, H. Priya and B. Srutha Keerth

Kocaeli University,
Faculty of Aviation and Space Sciences,
Arslanbey Campus, 41285 Kartepe-Kocaeli,
Turkey.
E-mail: serap.bulut@kocaeli.edu.tr

 
Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus, Chennai - 600 048,
India.
E-mail: priyaharikrishnan18@gmail.com, priya.h2020@vitstudent.ac.in

Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus, Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com, sruthakeerthi.b@vit.ac.in

Abstract:

In this paper, we introduce a new general subclass of analytic functions with respect to symmetric points in the domain of sine function. We obtain sharp coefficient bounds and upper bounds for the Fekete-Szegö functional. Also we get sharp bounds for the logarithmic coefficients of functions belonging to this new class.

Paper's Title:

Differential Sandwich Theorems for Some Subclasses of Analytic Functions

Author(s):

T. N. Shanmugam, V. Ravichandran and S. Sivasubramanian

Department of Mathematics, College of Engineering,
Anna university, Chennai 600 025,
India
shan@annauniv.edu
URL: http://www.annauniv.edu/shan

School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 USM Penang,
Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi

Department of Mathematics, Easwari Engineering college,
Ramapuram, Chennai 600 089,
India
sivasaisastha@rediffmail.com

Abstract:

Let and be univalent in with We give some applications of first order differential subordination and superordination to obtain sufficient conditions for normalized analytic function with to satisfy

Paper's Title:

Certain Coefficient Estimates for Bi-univalent Sakaguchi Type Functions

Author(s):

B. Srutha Keerthi, S. Chinthamani

Department of Applied Mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur, Chennai - 602105,
India

sruthilaya06@yahoo.co.in

 chinvicky@rediffmail.com

 

Abstract:

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f^-1 satisfying the conditions that zf'(z) / f(z) and zg'(z) / g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.

Paper's Title:

Hankel Functional Connected to Lemniscate of Bernoulli

Author(s):

K. Ramanuja Rao, Rajnesh Lal and Kaushal Singh

Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
E-mail: ramanuja.kotti@fnu.ac.fj
 rajnesh.lal@fnu.ac.fj
kaushal.singh@fnu.ac.fj

Abstract:

The aim of present paper is to derive a higher bound (HB) of 3^rd order Hankel determinant for a collection of holomorphic mappings connected with exactly to the right side of the lemniscate of Bernoulli, whose polar coordinates form is r² = 2cos²(2θ). The method carried in this paper is more refined than the method adopted by the authors (see [1]), who worked on this problem earlier.

Paper's Title:

Classes of Meromorphic p-valent Parabolic Starlike Functions with Positive Coefficients

Author(s):

S. Sivaprasad Kumar, V. Ravichandran, and G. Murugusundaramoorthy

Department of Applied Mathematics
Delhi College of Engineering,
Delhi 110042, India
sivpk71@yahoo.com

School of Mathematical Sciences
Universiti Sains Malaysia
11800 USM Penang
Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi

Department of Mathematics
Vellore Institute of Technology (Deemed University)
Vellore 632 014, India
gmsmoorthy@yahoo.com

Abstract:

In the present paper, we consider two general subclasses of meromorphic p-valent starlike functions with positive coefficients and obtain a necessary and sufficient condition for functions to be in these classes. Also we obtain certain other related results as a consequences of our main results.

Paper's Title:

Some Inequalities for a Certain Class of Multivalent Functions Using Multiplier Transformation

Author(s):

K. Suchithra, B. Adolf Stephen, A. Gangadharan and S. Sivasubramanian

Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai - 602105,
India.
suchithravenkat@yahoo.co.in

Department Of Mathematics,
Madras Christian College
Chennai - 600059,
India.
adolfmcc2003@yahoo.co.in

Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai - 602105,
India.
ganga@svce.ac.in

Department Of Mathematics,
Easwari Engineering College
Ramapuram, Chennai - 600089,
India.
ganga@svce.ac.in

Abstract:

The object of the present paper is to derive several inequalities associated with differential subordinations between analytic functions and a linear operator defined for a certain family of p-valent functions, which is introduced here by means of a family of extended multiplier transformations. Some special cases and consequences of the main results are also considered.

Paper's Title:

Fekete-Szegö Problem for Univalent Functions with Respect to k-Symmetric Points

Author(s):

K. Al-Shaqsi and M. Darus

School of Mathematical Sciences, Faculty of Science and Technology,
University Kebangsaan Malaysia,
Bangi 43600 Selangor D. Ehsan,
Malaysia
ommath@hotmail.com
maslina@ukm.my 

Abstract:

In the present investigation, sharp upper bounds of |a₃- μa₂²| for functions f(z) = z + a₂z² + a₂z³ + ... belonging to certain subclasses of starlike and convex functions with respect to k-symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete- Szegö inequalities for certain classes of functions defined through fractional derivatives are obtained.

Paper's Title:

On Sufficient Conditions for Strong Starlikeness

Author(s):

V. Ravichandran, M. H. Khan, M. Darus, And K. G. Subramanian

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Usm Penang, Malaysia
vravi@cs.usm.my
Url: http://cs.usm.my/~vravi/index.html

Department of Mathematics, Islamiah College, Vaniambadi 635 751, India
khanhussaff@yahoo.co.in

School of Mathematical Sciences, Faculty of Science and Technology, UKM, Bangi 43600,
Malaysia
maslina@pkrisc.cc.ukm.my
Url: http://www.webspawner.com/users/maslinadarus

Department of Mathematics, Madras Christian College, Tambaram, Chennai 600 059, India
kgsmani@vsnl.net

Abstract:

In the present investigation, we obtain some sufficient conditions for a normalized analytic function f(z) defined on the unit disk to satisfy the condition

Paper's Title:

On the Fekete-Szegő Inequality for Some Subclasses of Analytic Functions

Author(s):

T.N. Shanmugam and A. Singaravelu

Department of Mathematics,
College of Engineering,
Anna University, Chennai-600 025,
Tamilnadu, India
shan@annauniv.edu

Department of Mathematics,
Valliammai Engineering College,
Chennai-603 203,
Tamilnadu, India
sivasaisastha@rediffmail.com

Abstract:

In this present investigation, the authors obtainFekete-Szegő's inequality for certain normalized analytic functions defined on the open unit disk for which lie in a region starlike with respect to 1 and symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of this result, Fekete-Szegő's inequality for a class of functions defined through fractional derivatives is also obtained.

Paper's Title:

Generalized Hypergeometric Functions Defined on the Class of Univalent Functions

Author(s):

N. Marikkannan, A. Gangadharan and C. Ganesamoorthy

Department of Applied Mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur 602105,
India.
mari@svce.ac.in

Department of Applied mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur 602105,
India.
ganga@svce.ac.in

Department of Mathematics,
Alagappa university,
Karaikudi,
India.
ganesamoorthyc@yahoo.com

Abstract:

Let A denotes the class of all analytic functions f(z), normalized by the condition f'(0)-1=f(0)=0 defined on the open unit disk Δ and S be the subclass of A containing univalent functions of A. In this paper, we find the sufficient conditions for hypergeometric functions defined on S to be in certain subclasses of A, like k-UCV, k-ST

Paper's Title:

Subordination Results Associated with Hadamard Product

Author(s):

S. Sivasubramanian, C. Ramachandran and B. A. Frasin

Department of Mathematics,
University College of Engineering,
Anna University,
Saram-604 307,
India

sivasaisastha@rediffmail.com

Department of Mathematics,
University College of Engineering,
Anna University,
Villupuram,
India

crjsp2004@yahoo.com

Department of Mathematics,
Al al-Bayt University,
P.O. Box: 130095 Mafraq,
Jordan

bafrasin@yahoo.com


 

Abstract:

In the present investigation, we consider an unified class of functions of complex order using Hadamard's convolution. We obtain a necessary and sufficient condition for functions to be in these classes.

Paper's Title:

Sufficient Conditions for Certain Types of Functions to be Parabolic Starlike

Author(s):

A. Gangadharan and S. Chinthamani

Department of Mathematics,
Easwari Engineering College,
Ramapuram, Chennai - 89,
India.

Research Scholar,
Anna University,
Chennai

E-mail: ganga.megalai@gmail.com

E-mail: chinvicky@rediffmail.com

Abstract:

In this paper sufficient conditions are determined for functions of the form and certain other types of functions to be parabolic starlike.

Paper's Title:

Fekete-Szegö Inequality for Sakaguchi Type of functions in Petal Shaped Domain

Author(s):

E. K. Nithiyanandham and B. Srutha Keerthi

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: nithiyankrish@gmail.com

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com

Abstract:

In this paper, we estimate coefficient bounds,|a_2|,|a_3| and |a_4|, Fekete-Szegö inequality and Toeplitz determinant T₂(2) and T₃(1) for functions belonging to the following class

the function being holomorphic, we expand using Taylor series and obtain several corollaries and consequences for the main result.

Paper's Title:

Toeplitz Determinant for Sakaguchi Type Functions Under Petal Shaped Domain

Author(s):

B. Nandhini and B. Srutha Keerthi

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: nandhinibaskar1996@gmail.com

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com

Abstract:

We introduce a new general subclass GP^t,ρ of Sakaguchi kind function on a Petal shaped domain. We obtain coefficients bounds and upper bounds for the Fekete-Szegö functional over the class. From these functions we obtain the bounds of first four coefficients, and then we have derived the Toeplitz determinant T₂(2) and T₃(1) whose diagonal entries are the coefficients of functions.

Paper's Title:

A Subclass of Meromorphically Multivalent Functions with Applications to Generalized Hypergeometric Functions

Author(s):

M. K. Aouf

Mathematics Department, Faculty of Science,
Mansoura University 35516,
Egypt
mkaouf127@yahoo.com

Abstract:

In this paper a new subclass of meromorphically multivalent functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically p-valent functions. The main object of the present paper is to investigate the various important properties and characteristics of this subclass of meromorphically multivalent functions. We also derive many interesting results for the Hadamard products of functions belonging to this subclass. Also we consider several applications of our main results to generalized hypergeomtric functions.

Paper's Title:

On a subset of Bazilevic functions

Author(s):

Marjono and D. K. Thomas

Department of Mathematics,
Faculty of Mathematics and Natural Sciences,
Brawajaya University,
Malang, Jawa Timur 65145,
Indonesia.
E-mail: marjono@ub.ac.id

Department of Mathematics,
Swansea University, Singleton Park,
Swansea, SA2 8PP,
United Kingdom.
E-mail: d.k.thomas@swansea.ac.uk

Abstract:

Let S denote the class of analytic and univalent functions in of the form For α≥0, the subclass B₁α of S of Bazilevic functions has been extensively studied. In this paper we determine various properties of a subclass of B₁α, for α≥0 which extends early results of a class of starlike functions studied by Ram Singh.

Paper's Title:

Geometrical Properties of Subclass of Analytic Function with Odd Degree

Author(s):

K. Sivagami Sundari and B. Srutha Keerthi

Divison of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology, Chennai Campus, Chennai - 600 127,
India.
E-mail: sivagamisundari.2298@gmail.com 

Divison of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology, Chennai Campus, Chennai - 600 127,
India.
E-mail: keerthivitmaths@gmail.com
 

Abstract:

The objective of the paper is to study the geometrical properties of the class B(λ, t). For which we have proved that the radius is optimal ,(i.e) the number cannot be replaced by a larger one. Additionally, the graphs for various values of t and λ are compared in order to study the sharpness of the coefficient bounds.

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