scholarly journals Meromorphic Parabolic Starlike Functions Associated with q-Hypergeometric Series

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
T. Janani
Keyword(s):  
Fixed Point ◽  
Unit Disk ◽  
Hypergeometric Functions ◽  
Hypergeometric Series ◽  
Starlike Functions ◽  
Partial Sums ◽  
New Class ◽  
Coefficient Inequalities

We introduce a new class of meromorphic parabolic starlike functions with a fixed point defined in the punctured unit disk Δ*≔z∈ℂ:0<z<1 involving the q-hypergeometric functions. We obtained coefficient inequalities, growth and distortion inequalities, and closure results for functions f∈ℳmlλ,β,γ. We further established some results concerning convolution and the partial sums.

scholarly journals A new criterion for close-to-convexity of partial sums of certain hypergeometric functions

1997 ◽  
Vol 10 (2) ◽  
pp. 197-202
Author(s):  
Massoud Jahangiri
Keyword(s):  
Unit Disk ◽  
Hypergeometric Functions ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Criterion

We consider the partial sums of certain hypergeometric functions and establish conditions imposed on the locations of zeros of those polynomials in order to be close-to-convex in the open unit disk.

Coefficient inequalities for univalent starlike functions

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Milutin Obradović ◽  
Saminathan Ponnusamy
Keyword(s):  
Unit Disk ◽  
Complex Number ◽  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Right Hand ◽  
Coefficient Inequalities ◽  
The Right ◽  
Necessary And Sufficient

AbstractLet A be the class of analytic functions in the unit disk $$\mathbb{D}$$ with the normalization f(0) = f′(0) − 1 = 0. In this paper the authors discuss necessary and sufficient coefficient conditions for f ∈ A of the form $$\left( {\frac{z} {{f(z)}}} \right)^\mu = 1 + b_1 z + b_2 z^2 + \ldots$$ to be starlike in $$\mathbb{D}$$ and more generally, starlike of some order β, 0 ≤ β < 1. Here µ is a suitable complex number so that the right hand side expression is analytic in $$\mathbb{D}$$ and the power is chosen to be the principal power. A similar problem for the class of convex functions of order β is open.

SOME NEW RESULTS ASSOCIATED WITH CARATHÉODORY FUNCTIONS OF ORDER α

2016 ◽  
Vol 2 (1) ◽  
pp. 11-13
Author(s):  
H. M. Srivastava ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Extremal Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
Carathéodory Functions ◽  
Coefficient Inequalities ◽  
The Extremal Function ◽  
Class Of Functions

Let $\mathcal{P}(\alpha)$ be the class of functions $p(z)$ which are Carathéodory functions of order $\alpha$ $(0 \le\alpha<1)$ in the open unit disk $\mathbf{U}$. Considering the extremal function $p(z)$ for the class $\mathcal{P}(\alpha)$, a new class ${\mathcal P}^*(\beta)$ $\beta\in \mathbb{R}$ of functions $q(z)$ in $\mathbf{U}$ is defined. The object of the present paper is to develop several interesting coefficient inequalities for the functions $q(z)$ in the new class $\mathcal{P}^*(\beta)$ introduced here.

scholarly journals On Certain Sufficient Condition Involving Gaussian Hypergeometric Functions

2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
H. Silverman ◽  
Thomas Rosy ◽  
S. Kavitha
Keyword(s):  
Unit Disk ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
New Class ◽  
Inclusion Properties ◽  
Complex Order ◽  
Gaussian Hypergeometric Functions

The authors define a new subclass of of functions involving complex order in the open unit disk . For this new class, we obtain certain inclusion properties involving the Gaussian hypergeometric functions.

scholarly journals A class of bounded starlike functions

1994 ◽  
Vol 17 (2) ◽  
pp. 249-252 ◽  
Author(s):  
Herb Silverman
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Extreme Points ◽  
Starlike Functions ◽  
Partial Sums

We consider functionsf(z)=z+…that are analytic in the unit disk and satisfy there the inequalityRe(f′(z)+zf″(z))>α,α<1. We find extreme points and then determine sharp lower bounds onRef′(z)andRe(f(z)/z). Sharp results for the sequence of partial sums are also found.

Certain classes of analytic functions defined by Hurwitz–Lerch zeta function

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Bolineni Venkateswarlu ◽  
Pinninti Thirupathi Reddy ◽  
Galla Swapna ◽  
Rompilli Madhuri Shilpa
Keyword(s):  
Zeta Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
New Class ◽  
Lerch Zeta Function

Abstract In this work, we introduce and investigate a new class k - U ⁢ S ~ s ⁢ ( b , μ , γ , t ) {k-\widetilde{US}_{s}(b,\mu,\gamma,t)} of analytic functions in the open unit disk U with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions f belonging to this class.

scholarly journals On q-Starlike Functions Defined by q-Ruscheweyh Differential Operator in Symmetric Conic Domain

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1947
Author(s):  
Saira Zainab ◽  
Mohsan Raza ◽  
Qin Xin ◽  
Mehwish Jabeen ◽  
Sarfraz Nawaz Malik ◽  
...  
Keyword(s):  
Differential Operator ◽  
Starlike Functions ◽  
Partial Sums ◽  
Open Unit ◽  
New Class ◽  
Conic Domain ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Coefficient Bound ◽  
Necessary And Sufficient

Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to first define and then study a new class of holomorphic functions using the q-Ruscheweyh differential operator. A new class k−STqτC,D of k-Janowski starlike functions associated with the symmetric conic domain, which are defined by the generalized Ruscheweyh derivative operator in the open unit disk, is introduced. The necessary and sufficient condition for a function to be in the class k−STqτC,D is established. In addition, the coefficient bound, partial sums and radii of starlikeness for the functions from the class of k-Janowski starlike functions related with symmetric conic domain are included.

scholarly journals Starlike functions of complex order involving q-hypergeometric functions with fixed point

2014 ◽  
Vol 13 (1) ◽  
pp. 51-63
Author(s):  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Murugesan Kasthuri
Keyword(s):  
Fixed Point ◽  
Hypergeometric Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Function Class ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Open Disc ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractRecently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ).

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

Coefficient inequalities related with typically real functions

2020 ◽  
Vol 70 (4) ◽  
pp. 829-838
Author(s):  
Saqib Hussain ◽  
Shahid Khan ◽  
Khalida Inayat Noor ◽  
Mohsan Raza
Keyword(s):  
Unit Disk ◽  
Real Functions ◽  
Coefficient Inequalities ◽  
Typically Real ◽  
Class Of Functions ◽  
Typically Real Functions

AbstractIn this paper, we are mainly interested to study the generalization of typically real functions in the unit disk. We study some coefficient inequalities concerning this class of functions. In particular, we find the Zalcman conjecture for generalized typically real functions.

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