A Certain Subclass of Analytic Functions with Negative Coefficients Defined by Gegenbauer Polynomials

2021 ◽  
Vol 78 (1) ◽  
pp. 73-84
Author(s):  
Bolineni Venkateswarlu ◽  
Pinninti Thirupathi Reddy ◽  
Settipalli Sridevi ◽  
Vaishnavy Sujatha
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Gegenbauer Polynomials ◽  
Coefficient Bounds

Abstract In this paper, we introduce a new subclass of analytic functions with negative coefficients defined by Gegenbauer polynomials. We obtain coefficient bounds, growth and distortion properties, extreme points and radii of starlikeness, convexity and close-to-convexity for functions belonging to the class T S λ m ( γ , e , k , v ) TS_\lambda ^m(\gamma ,e,k,v) . Furthermore, we obtained the Fekete-Szego problem for this class.

scholarly journals Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

2021 ◽  
pp. 49-76
Author(s):  
Faroze Ahmad Malik ◽  
Nusrat Ahmed Dar ◽  
Chitaranjan Sharma
Keyword(s):  
Convex Functions ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Integral Operators ◽  
Integral Means ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Special Cases ◽  
The Family

We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.

scholarly journals Certain convex harmonic functions

2002 ◽  
Vol 29 (8) ◽  
pp. 459-465 ◽  
Author(s):  
Yong Chan Kim ◽  
Jay M. Jahangiri ◽  
Jae Ho Choi
Keyword(s):  
Analytic Functions ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Uniformly Convex ◽  
Coefficient Bounds ◽  
Distortion Theorems ◽  
Harmonic Convex ◽  
Complex Valued ◽  
Convex Univalent Functions

We define and investigate a family of complex-valued harmonic convex univalent functions related to uniformly convex analytic functions. We obtain coefficient bounds, extreme points, distortion theorems, convolution and convex combinations for this family.

Extreme points of families of analytic functions subordinate to convex mappings

1981 ◽  
Vol 176 (4) ◽  
pp. 511-519 ◽  
Author(s):  
Yusuf Abu-Muhanna ◽  
Thomas H. MacGregor
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Convex Mappings

scholarly journals Coefficients estimates of some subclasses of analytic functions related with conic domain

2013 ◽  
Vol 21 (2) ◽  
pp. 181-188 ◽  
Author(s):  
Sarfraz Nawaz Malik ◽  
Mohsan Raza ◽  
Muhammad Arif ◽  
Saqib Hussain
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Coefficient Bounds ◽  
Conic Domain

Abstract In this paper, the authors determine the coefficient bounds for functions in certain subclasses of analytic functions related with the conic regions, which are introduced by using the concept of bounded boundary and bounded radius rotations. The effect of certain integral operator on these classes has also been examined.

scholarly journals Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Akhter Rasheed ◽  
Saqib Hussain ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

scholarly journals Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 719 ◽  
Author(s):  
Shahid Mahmood ◽  
Nusrat Raza ◽  
Eman S. A. AbuJarad ◽  
Gautam Srivastava ◽  
H. M. Srivastava ◽  
...  
Keyword(s):  
Integral Operator ◽  
Bessel Function ◽  
Analytic Functions ◽  
Operator Coefficient ◽  
Geometric Properties ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Inclusion Relations

This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ ( γ ∈ C \ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by using this q-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the ( δ , q )-neighborhood of analytic functions are introduced and the inclusion relations between the ( δ , q )-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed.

scholarly journals EXTREME POINTS OF INTEGRAL FAMILIES OF ANALYTIC FUNCTIONS

2013 ◽  
Vol 94 (2) ◽  
pp. 202-221
Author(s):  
KEIKO DOW ◽  
D. R. WILKEN
Keyword(s):  
Analytic Functions ◽  
Compact Convex ◽  
Extreme Points ◽  
Starlike Functions ◽  
Extremal Problems ◽  
Kernel Functions ◽  
Closed Convex Hull ◽  
New Class ◽  
Geometric Function ◽  
Derivatives Of

AbstractExtreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a two-parameter collection of kernel functions integrated against measures on the torus. For specific choices of the parameters many families from classical geometric function theory are included. These families include the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others. The main result introduces a surprising new class of extreme points.

scholarly journals The Extreme and Support Points of a New Class of Analytic Functions with Positive Real Part

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Zhigang Peng
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Positive Real Part ◽  
Positive Real ◽  
New Class ◽  
Support Points

Suppose that 0<α<β<+∞. Let 𝒫(α,β) denote the set of functions p(z) that are analytic in D= {z:|z|<1}  and satisfy Rep(z)>0(|z|<1) and α≤p(0)≤β. In this paper, we investigate the extreme points and support points of 𝒫(α,β).

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