On Booth Lemniscate and Hadamard Product of Analytic Functions

2015 ◽  
Vol 65 (6) ◽  
Author(s):  
Krzysztof Piejko ◽  
Janusz Sokół
Keyword(s):  
Convex Hull ◽  
Hadamard Product ◽  
Special Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Convex Mappings ◽  
Geometric Function ◽  
Booth Lemniscate ◽  
New Applications ◽  
Convex Univalent Functions

AbstractIn [RUSCHEWEYH, S.-SHEIL-SMALL, T.: Hadamard product of schlicht functions and the Poyla-Schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119-135] the authors proved the P`olya-Schoenberg conjecture that the class of convex univalent functions is preserved under convolution, namely K ∗ K = K. They proved also that the class of starlike functions and the class of close-to-convex functions are closed under convolution with the class K. In this paper we consider similar convolution problems for some classes of functions. Especially we give a new applications of a result [SOKÓŁ, J.: Convolution and subordination in the convex hull of convex mappings, Appl. Math. Lett. 19 (2006), 303-306] on the subordinating relations in the convex hull of convex mappings under convolution. The paper deals with several ideas and techniques used in geometric function theory. Besides being an application to those results it provides interesting corollaries concerning special functions, regions and curves.

scholarly journals Analytic Univalent Functions Defined by Generalized Discrete Probability Distribution

2020 ◽  
pp. 169-178
Author(s):  
Abiodun Tinuoye Oladipo
Keyword(s):  
Probability Distribution ◽  
Function Theory ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Geometric Function Theory ◽  
Strong Connection ◽  
Discrete Probability ◽  
Discrete Probability Distribution ◽  
Geometric Function ◽  
Coefficient Inequalities

The close-to-convex analogue of a starlike functions by means of generalized discrete probability distribution and Poisson distribution was considered. Some coefficient inequalities and their connection to classical Fekete-Szego theorem are obtained. Our results provide strong connection between Geometric Function Theory and Statistics.

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

scholarly journals Fuzzy Differential Subordinations Based Upon the Mittag-Leffler Type Borel Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1023
Author(s):  
Hari Mohan Srivastava ◽  
Sheza M. El-Deeb
Keyword(s):  
Fuzzy Systems ◽  
Special Functions ◽  
Univalent Functions ◽  
Local Symmetry ◽  
Open Unit ◽  
Fuzzy Membership Functions ◽  
Non Local ◽  
Differential Subordinations ◽  
Two Parameter ◽  
Borel Type

In this paper, we investigate several fuzzy differential subordinations that are connected with the Borel distribution series Bλ,α,β(z) of the Mittag-Leffler type, which involves the two-parameter Mittag-Leffler function Eα,β(z). Using the above-mentioned operator Bλ,α,β, we also introduce and study a class Mλ,α,βFη of holomorphic and univalent functions in the open unit disk Δ. The Mittag-Leffler-type functions, which we have used in the present investigation, belong to the significantly wider family of the Fox-Wright function pΨq(z), whose p numerator parameters and q denominator parameters possess a kind of symmetry behavior in the sense that it remains invariant (or unchanged) when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. Here, in this article, we have used such special functions in our study of a general Borel-type probability distribution, which may be symmetric or asymmetric. As symmetry is generally present in most works involving fuzzy sets and fuzzy systems, our usages here of fuzzy subordinations and fuzzy membership functions potentially possess local or non-local symmetry features.

scholarly journals Further Results for Starlike Functions Related with Booth Lemniscate

2018 ◽  
Vol 43 (3) ◽  
pp. 1235-1238 ◽  
Author(s):  
Rahim Kargar ◽  
Ali Ebadian ◽  
Lucyna Trojnar-Spelina
Keyword(s):  
Starlike Functions ◽  
Booth Lemniscate

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

scholarly journals On new applications of fractional calculus

2017 ◽  
Vol 37 (3) ◽  
pp. 113-118 ◽  
Author(s):  
Shilpi Jain ◽  
Praveen Agarwal
Keyword(s):  
Fractional Calculus ◽  
Special Functions ◽  
Leibniz Rule ◽  
The One ◽  
New Applications ◽  
Paper Author

In the present paper author derive a number of integrals concerning various special functions which are applications of the one of Osler result. Osler provided extensions to the familiar Leibniz rule for the nth derivative of product of two functions.

scholarly journals On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals Region of Variability for Exponentially Convex Univalent Functions

2010 ◽  
Vol 5 (3) ◽  
pp. 955-966 ◽  
Author(s):  
Ponnusamy Saminathan ◽  
Vasudevarao Allu ◽  
M. Vuorinen
Keyword(s):  
Univalent Functions ◽  
Convex Univalent Functions
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