On generalized gamma-Bazilevic functions

2020 ◽  
pp. 2150093
Author(s):  
Khalida Inayat Noor ◽  
Shujaat Ali Shah ◽  
Afis Saliu
Keyword(s):  
Covering Theorem ◽  
Generalized Gamma ◽  
Bazilevic Functions ◽  
Radius Problem ◽  
Inclusion Results

In this paper, we define and study the class [Formula: see text] of generalized gamma-Bazilevic functions. Our main focus is to discuss certain problems such as inclusion results, covering theorem and radius problem.

scholarly journals Some classes of p-valent analytic functions associated with hypergeometric functions

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1031-1038 ◽  
Author(s):  
Khalida Noor ◽  
Nasir Khan
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Class A ◽  
Radius Problem ◽  
Inclusion Results

We define a linear operator on the class A(p) of p-valent analytic functions in the open unit disc involving Gauss hypergeometric functions and introduce certain new subclasses of A(p) using this operator. Some inclusion results, a radius problem and several other interesting properties of these classes are studied.

scholarly journals On Uniformly Bazilevic and Related Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Open Unit ◽  
Arc Length ◽  
Open Unit Disc ◽  
New Class ◽  
Univalence Criterion ◽  
Distortion Bounds ◽  
Special Cases ◽  
Bazilevic Functions ◽  
Class Of Functions ◽  
Inclusion Results

We introduce a new class of functions analytic in the open unit disc, which contains the class of Bazilevic functions and also generalizes the concept of uniform convexity. We establish univalence criterion for the functions in this class and investigate rate of growth of coefficients, arc length problem, inclusion results, and distortion bounds. Some interesting results are derived as special cases.

scholarly journals Coefficient inequalities for a subclass of Bazilevič functions

2020 ◽  
Vol 53 (1) ◽  
pp. 27-37
Author(s):  
Sa’adatul Fitri ◽  
Derek K. Thomas ◽  
Ratno Bagus Edy Wibowo ◽  
Keyword(s):  
Recent Work ◽  
Sharp Bounds ◽  
Coefficient Problems ◽  
Coefficient Inequalities ◽  
Bazilevic Functions

AbstractLet f be analytic in {\mathbb{D}}=\{z:|z\mathrm{|\hspace{0.17em}\lt \hspace{0.17em}1\}} with f(z)=z+{\sum }_{n\mathrm{=2}}^{\infty }{a}_{n}{z}^{n}, and for α ≥ 0 and 0 < λ ≤ 1, let { {\mathcal B} }_{1}(\alpha ,\lambda ) denote the subclass of Bazilevič functions satisfying \left|f^{\prime} (z){\left(\frac{z}{f(z)}\right)}^{1-\alpha }-1\right|\lt \lambda for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f\in { {\mathcal B} }_{1}(\alpha ,\lambda ), thus extending recent work in the case λ = 1.

scholarly journals The Approximation of the Nonlinear Singular System with Impulses and Sliding Mode Control via a Singular Polynomial Fuzzy Model Approach

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1409
Author(s):  
Jiawen Li ◽  
Yi Zhang ◽  
Zhenghong Jin
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Singular System ◽  
Fuzzy Model ◽  
Switching Function ◽  
Covering Theorem ◽  
Function Type ◽  
Numerical Examples ◽  
Mode Control ◽  
Nonlinear Singular System

In this paper, the Singular-Polynomial-Fuzzy-Model (SPFM) approach problem and impulse elimination are investigated based on sliding mode control for a class of nonlinear singular system (NSS) with impulses. Considering two numerical examples, the SPFM of the nonlinear singular system is calculated based on the compound function type and simple function type. According to the solvability and the steps of two numerical examples, the method of solving the SPFM form of the nonlinear singular system with (and without) impulse are extended to the more general case. By using the Heine–Borel finite covering theorem, it is proven that a class of nonlinear singular systems with bounded impulse-free item (BIFI) properties and separable impulse item (SII) properties can be approximated by SPFM with arbitrary accuracy. The linear switching function and sliding mode control law are designed to be applied to the impulse elimination of SPFM. Compared with some published works, a human posture inverted pendulum model example and Example 3.2 demonstrate that the approximation error is small enough and that both algorithms are effective. Example 3.3 is to illustrate that sliding mode control can effectively eliminate impulses of SPFM.

scholarly journals On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1571
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Law Of Large Numbers ◽  
Negative Binomial ◽  
Infinite Divisibility ◽  
Random Sums ◽  
Generalized Gamma ◽  
Second Moments ◽  
Large Numbers ◽  
Generalized Negative Binomial Distribution

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

scholarly journals Poisson generalized gamma process and its properties

Stochastics ◽  
2021 ◽  
pp. 1-18
Author(s):  
Ji Hwan Cha ◽  
Sophie Mercier
Keyword(s):  
Gamma Process ◽  
Generalized Gamma

scholarly journals Generalized Gamma – Generalized Gompertz Distribution

2020 ◽  
Vol 1591 ◽  
pp. 012043
Author(s):  
M A A Boshi ◽  
S H Abid ◽  
N H Al-Noor
Keyword(s):  
Gompertz Distribution ◽  
Generalized Gamma
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