scholarly journals Coefficient Inequalities of Functions Associated with Hyperbolic Domains

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 88 ◽  
Author(s):  
Sarfraz Malik ◽  
Shahid Mahmood ◽  
Mohsan Raza ◽  
Sumbal Farman ◽  
Saira Zainab ◽  
...  
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Image Domain ◽  
Coefficient Inequalities ◽  
Inverse Functions ◽  
Hyperbolic Domains

In this work, our focus is to study the Fekete-Szegö functional in a different and innovative manner, and to do this we find its upper bound for certain analytic functions which give hyperbolic regions as image domain. The upper bounds obtained in this paper give refinement of already known results. Moreover, we extend our work by calculating similar problems for the inverse functions of these certain analytic functions for the sake of completeness.

scholarly journals Coefficient Inequalities of Functions Associated with Petal Type Domains

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 298 ◽  
Author(s):  
Sarfraz Malik ◽  
Shahid Mahmood ◽  
Mohsan Raza ◽  
Sumbal Farman ◽  
Saira Zainab
Keyword(s):  
Taylor Series ◽  
Upper Bound ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Series Representation ◽  
Functional Inequalities ◽  
Major Interest ◽  
Coefficient Inequalities ◽  
Inverse Functions ◽  
Analytic And Univalent Functions

In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains. One of the important and useful functional inequalities is the Fekete-Szegö inequality. In this work, we aim to analyze the Fekete-Szegö functional and to find its upper bound for certain analytic functions which give parabolic and petal type regions as image domains. Coefficient inequalities and the Fekete-Szegö inequality of inverse functions to these certain analytic functions are also established in this work.

scholarly journals Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

2018 ◽  
Vol 37 (4) ◽  
pp. 83-95
Author(s):  
Trailokya Panigrahi ◽  
Janusz Sokól
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
Toeplitz Determinant ◽  
Second Hankel Determinant ◽  
Coefficient Inequalities ◽  
The Right

In this paper, a new subclass of analytic functions ML_{\lambda}^{*}  associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}|  for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

scholarly journals Extremal Problems for Functions Starlike in the Exterior of the Unit Circle

1962 ◽  
Vol 14 ◽  
pp. 540-551 ◽  
Author(s):  
W. C. Royster
Keyword(s):  
Unit Circle ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Extremal Problems ◽  
Simple Pole ◽  
Image Position ◽  
Inverse Functions ◽  
Variational Formulas

Let Σ represent the class of analytic functions(1)which are regular, except for a simple pole at infinity, and univalent in |z| > 1 and map |z| > 1 onto a domain whose complement is starlike with respect to the origin. Further let Σ- 1 be the class of inverse functions of Σ which at w = ∞ have the expansion(2).In this paper we develop variational formulas for functions of the classes Σ and Σ- 1 and obtain certain properties of functions that extremalize some rather general functionals pertaining to these classes. In particular, we obtain precise upper bounds for |b2| and |b3|. Precise upper bounds for |b1|, |b2| and |b3| are given by Springer (8) for the general univalent case, provided b0 =0.

scholarly journals Kth Root Transformation for a subclass of Log-Sigmoid Analytic Function based on Quasi-Subordination

2018 ◽  
Vol 7 (4.10) ◽  
pp. 1007
Author(s):  
M. Hari Priya ◽  
R. Bharavi Sharma ◽  
V. Suman Kumar
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Root Transformation ◽  
Coefficient Inequalities

In the present investigation, using the concept of quasi-subordination, two subclasses of analytic functions have been introduced. The coefficient inequalities, the Fekete-Szego inequality, upper bounds for kth  root transformation were studied. This study is extended to function  and for  . 

scholarly journals Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ming-Sheng Liu ◽  
Jun-Feng Xu ◽  
Ming Yang
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
Work Done

In this present investigation, we first give a survey of the work done so far in this area of Hankel determinant for univalent functions. Then the upper bounds of the second Hankel determinant|a2a4−a32|for functions belonging to the subclassesS(α,β),K(α,β),Ss∗(α,β), andKs(α,β)of analytic functions are studied. Some of the results, presented in this paper, would extend the corresponding results of earlier authors.

Third Hankel determinants for two classes of analytic functions with real coefficients

2021 ◽  
Vol 33 (4) ◽  
pp. 973-986
Author(s):  
Young Jae Sim ◽  
Paweł Zaprawa
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Lower And Upper Bounds ◽  
Hankel Determinants ◽  
The Third ◽  
Typically Real ◽  
Class Of Functions ◽  
Typically Real Functions

Abstract In recent years, the problem of estimating Hankel determinants has attracted the attention of many mathematicians. Their research have been focused mainly on deriving the bounds of H 2 , 2 {H_{2,2}} or H 3 , 1 {H_{3,1}} over different subclasses of 𝒮 {\mathcal{S}} . Only in a few papers third Hankel determinants for non-univalent functions were considered. In this paper, we consider two classes of analytic functions with real coefficients. The first one is the class 𝒯 {\mathcal{T}} of typically real functions. The second object of our interest is 𝒦 ℝ ⁢ ( i ) {\mathcal{K}_{\mathbb{R}}(i)} , the class of functions with real coefficients which are convex in the direction of the imaginary axis. In both classes, we find lower and upper bounds of the third Hankel determinant. The results are sharp.

Upper bounds on the energy dissipation in turbulent precession

1996 ◽  
Vol 321 ◽  
pp. 335-370 ◽  
Author(s):  
R. R. Kerswell
Keyword(s):  
Experimental Data ◽  
Energy Dissipation ◽  
Viscous Dissipation ◽  
Upper Bound ◽  
Dissipation Rate ◽  
Oblate Spheroid ◽  
Upper Bounds ◽  
Precession Rate ◽  
Long Cylinder

Rigorous upper bounds on the viscous dissipation rate are identified for two commonly studied precessing fluid-filled configurations: an oblate spheroid and a long cylinder. The latter represents an interesting new application of the upper-bounding techniques developed by Howard and Busse. A novel ‘background’ method recently introduced by Doering & Constantin is also used to deduce in both instances an upper bound which is independent of the fluid's viscosity and the forcing precession rate. Experimental data provide some evidence that the observed viscous dissipation rate mirrors this behaviour at sufficiently high precessional forcing. Implications are then discussed for the Earth's precessional response.

scholarly journals The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

2012 ◽  
Vol 10 (3) ◽  
pp. 455-488 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon ◽  
Nicole Lemire
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Vector Bundles ◽  
Upper Bounds ◽  
Essential Dimension ◽  
Parabolic Structure ◽  
Moduli Stack

AbstractWe find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.

ances and covariances obtained from REML are normally distributed with expectation vector and variance-covariance matrix equal to the fol-low  ing, r  espectiv    ely,   When σˆ > 0.04, let νˆ = δˆ + σˆ + σˆ − 2ωˆ + σˆ − (1 + c (7.6) be an estimate for the (7.3) reference-scaled metric in accordance with FDA Guidance (2001) and using a REML UN model. Then (Patter-son, 2003; Patterson and Jones, 2002b), this estimate is asymptotically normally distributed and unbiased with E[νˆ ] = δ +σ − (1 + c and Var[νˆ ] = 4σ + l + 4l + (1 + c ) (l )+ 2l −2(1+c − 2(1+c +4(1+c −2(1+c . Similarly, for the constant-scaled metric, when σˆ ≤ 0.04, νˆ = δˆ + σˆ + σˆ − 2ωˆ + σˆ − σˆ − 0.04(c ) (7.7) E[νˆ ] = δ +σ − 0.04(c ) Var[νˆ ] = 4σ + l + 4l + 2l − 2l − 4l + 4l − 2l . The required asymptotic upper bound √ of the 90% confidence interval can √ then be calculated as νˆ + 1.645× V̂ ar[νˆ ] or νˆ + 1.645× V̂ ar[νˆ ], where the variances are obtained by ‘plugging in’ the estimated values of the variances and covariances obtained from SAS proc mixed into the formulae for Var[νˆ ] or Var[νˆ ]. The necessary SAS code to do this is given in Appendix B. The output reveals that σˆ = 0.0714 and the upper bound is−0.060 for log(AUC). For log(Cmax), σˆ = 0.1060 and the upper bound is −0.055. As both of these upper bounds are below zero, IBE can be claimed.

2003 ◽  
pp. 367-367
Keyword(s):  
Confidence Interval ◽  
Covariance Matrix ◽  
Upper Bound ◽  
Upper Bounds ◽  
Fda Guidance ◽  
Asymptotic Upper Bound ◽  
Variance Covariance Matrix ◽  
Normally Distributed

scholarly journals Hankel determinant for a class of analytic functions of complex order defined by convolution

2015 ◽  
Vol 69 (2) ◽  
pp. 47
Author(s):  
S. M. El-Deeb ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Complex Order ◽  
Second Hankel Determinant

In this paper, we obtain the Fekete-Szego inequalities for the functions of complex order defined by convolution. Also, we find upper bounds for the second Hankel determinant \(|a_2a_4-a_3^2|\) for functions belonging to the class \(S_{\gamma}^b(g(z);A,B)\).

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