Rate of convergence of the Taylor series for some classes of analytic functions

1998 ◽  
Vol 50 (7) ◽  
pp. 1141-1144 ◽  
Author(s):  
V. V. Savchuk
Keyword(s):  
Rate Of Convergence ◽  
Taylor Series ◽  
Analytic Functions

scholarly journals Bounds on the Third Order Hankel Determinant for Certain Subclasses of Analytic Functions

2017 ◽  
Vol 25 (3) ◽  
pp. 199-214
Author(s):  
S.P. Vijayalakshmi ◽  
T.V. Sudharsan ◽  
Daniel Breaz ◽  
K.G. Subramanian
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Analytic Functions ◽  
Unit Disc ◽  
Taylor Series Expansion ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Third Order ◽  
The Third

Abstract Let A be the class of analytic functions f(z) in the unit disc ∆ = {z ∈ C : |z| < 1g with the Taylor series expansion about the origin given by f(z) = z+ ∑n=2∞ anzn, z ∈∆ : The focus of this paper is on deriving upper bounds for the third order Hankel determinant H3(1) for two new subclasses of A.

scholarly journals The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-19
Author(s):  
Wolf Bayer
Keyword(s):  
Differential Operator ◽  
Taylor Series ◽  
Analytic Functions ◽  
Chaotic Behavior ◽  
Higher Order ◽  
Limit Behavior ◽  
Hyperbolic Functions ◽  
Limit Sets ◽  
The Common

For analytic functions, we investigate the limit behavior of the sequence of their derivatives by means of Taylor series, the attractors are characterized by -limit sets. We describe four different classes of functions, with empty, finite, countable, and uncountable attractors. The paper reveals that Erdelyiéshyperbolic functions of higher orderandlacunary functionsplay an important role for orderly or chaotic behavior. Examples are given for the sake of confirmation.

scholarly journals Approximation by complex modified Szász-Mirakjan-Stancu operators in compact disks

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1007-1019 ◽  
Author(s):  
Nursel Çetin
Keyword(s):  
Rate Of Convergence ◽  
Exponential Growth ◽  
Analytic Functions ◽  
Exact Order ◽  
Order Of Approximation ◽  
Stancu Operators ◽  
Exact Order Of Approximation ◽  
Compact Disks

In this paper, we establish some theorems on approximation and Voronovskaja type results for complex modified Sz?sz-Mirakjan-Stancu operators attached to analytic functions having exponential growth on compact disks. Also, we estimate the rate of convergence and the exact order of approximation.

scholarly journals On Koenig's theorem for integer functions of finite order

2020 ◽  
pp. 280-289
Author(s):  
А.Н. Громов
Keyword(s):  
Convergence Rate ◽  
Rate Of Convergence ◽  
Finite Order ◽  
Analytic Functions ◽  
Measure Zero ◽  
Logarithmic Derivative ◽  
Convergence Domain ◽  
Globally Convergent ◽  
Voronoi Polygons ◽  
Zeros Of Analytic Functions

Показано, что теорема Кенига о нулях аналитической функции, примененная к логарифмической производной целой функции конечного порядка, приводит к алгоритму отыскания нулей, для которого областями сходимости являются многоугольники Вороного искомых нулей. Так как диаграмма Вороного последовательности нулей составляет множество меры нуль, то алгоритм имеет глобальную сходимость. Дана оценка скорости сходимости. Для итераций высших порядков, которые строятся с помощью теоремы Кенига, рассмотрено влияние кратности корня на область сходимости и приводится оценка скорости сходимости. It is shown that Koenig's theorem on zeros of analytic functions applied to the logarithmic derivative of an integer function of finite order leads to an algorithm of finding zeros whose convergence domains are the Voronoi polygons of the zeros to be found. Since the Voronoi diagram of a sequence of zeros is a set of measure zero, this algorithm is globally convergent. The rate of convergence is estimated. For higher-order iterations that are constructed using Koenig's theorem, the effect of root multiplicity on the convergence domain is considered and the convergence rate is estimated for this case.

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 a*-families of analytic functions

1984 ◽  
Vol 7 (3) ◽  
pp. 435-442 ◽  
Author(s):  
G. P. Kapoor ◽  
A. K. Mishra
Keyword(s):  
Analytic Function ◽  
Taylor Series ◽  
Analytic Functions ◽  
Extreme Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
New Family ◽  
Symmetric Points ◽  
Necessary And Sufficient

Using convolutions, a new family of analytic functions is introduced. This family, calleda*-family, serves in certain situations to unify the study of many previously well known classes of analytic functions like multivalent convex, starlike, close-to-convex or prestarlike functions, functions starlike with respect to symmetric points and other such classes related to the class of univalent or multivalent functions. A necessary and sufficient condition on the Taylor series coefficients so that an analytic function with negative coefficients is in ana*-family is obtained and sharp coefficents bound for functions in such a family is deduced. The extreme points of ana*-family of functions with negative coefficients are completely determined. Finally, it is shown that Zmorvic conjecture is true if the concerned families consist of functions with negative coefficients.

scholarly journals AN ITERATIVE FORMULA FOR SIMULTANEOUS LOCATION OF THE ZEROS OF A POLYNOMIAL

2021 ◽  
Vol 5 (12) ◽  
Author(s):  
Dr.Abdel Wahab Nourein
Keyword(s):  
Rate Of Convergence ◽  
Series Expansion ◽  
Taylor Series ◽  
Iteration Method ◽  
Taylor Series Expansion ◽  
Efficient Algorithms ◽  
Zeros Of Polynomials ◽  
Correction Terms

Needless to say that the search for efficient algorithms for determining zeros of polynomials has been continually raised in many applications. In this paper we give a cubic iteration method for determining simultaneously all the zeros of a polynomial – assumed distinct – starting with ‘reasonably close’ initial approximations – also assumed distinct. The polynomial – in question – is expressed in its Taylor series expansion in terms of the initial approximations and their correction terms. A formula with cubic rate of convergence – based on retaining terms up to 2ndorder of the expansion in the correction terms – is derived.

scholarly journals Approximation of analytic functions by linear methods of summation of Taylor series

2018 ◽  
Vol 2018 (1) ◽  
pp. 33-46
Author(s):  
Mykola A. Veremii ◽  
Mykola V. Haevskyi ◽  
Petro V. Zaderei
Keyword(s):  
Taylor Series ◽  
Analytic Functions
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