Partial sums of analytic functions of bounded turning with applications

Darus, Maslina; Ibrahim, Rabha W.

doi:10.1590/s1807-03022010000100006

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Introduction2

Example 1 (See Figs 1 and 2)1

Partial Sums1

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Cited by 14 publications

(8 citation statements)

References 9 publications

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“…There are different techniques of studying the class of bounded turning functions, such as using partial sums or applying Jack Lemma [5]- [7].…”

Section: Example 1 (See Figs 1 and 2)mentioning

confidence: 99%

Univalent Functions Formulated by the Salagean-Difference Operator

2019

ijaa

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We present a class of univalent functions Tm(κ, α) formulated by a new differential-difference operator in the open unit disk. The operator is a generalization of the well known Salagean's differential operator. Based on this operator, we define a generalized class of bounded turning functions. Inequalities, extreme points of Tm(κ, α), some convolution properties of functions fitting to Tm(κ, α), and other properties are discussed.

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“…There are different techniques of studying the class of bounded turning functions, such as using partial sums or applying Jack Lemma [5]- [7].…”

Section: Example 1 (See Figs 1 and 2)mentioning

confidence: 99%

Univalent Functions Formulated by the Salagean-Difference Operator

2019

ijaa

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“…Recently, Darus and Ibrahim [4] and Hayami et al [5] have shown some interesting results for some partial sums of analytic functions. Now, we derive the following.…”

Section: Partial Sumsmentioning

confidence: 99%

New Subclasses concerning Some Analytic and Univalent Functions

Darus

Owa

2017

Chinese Journal of Mathematics

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“…In addition, Darus and Ibrahim [11] specified the assumptions, which indicated that the partial sums of functions of bounded turning are also of bounded turning. Recently, Darus and Ibrahim [12] …”

Section: Introductionmentioning

confidence: 99%

Upper Bound of Partial Sums Determined by Matrix Theory

Ibrahim¹

2016

TJANT

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One of the major problems in the geometric function theory is the coefficients bound for functional and partial sums. The important method, for this purpose, is the Hankel matrix. Our aim is to introduce a new method to determine the coefficients bound, based on the matrix theory. We utilize various kinds of matrices, such as Hilbert, Hurwitz and Turan. We illustrate new classes of analytic function in the unit disk, depending on the coefficients of a particular type of partial sums. This method shows the effectiveness of the new classes. Our results are applied to the well known classes such as starlike and convex. One can illustrate the same method on other classes.

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Partial sums of analytic functions of bounded turning with applications

Abstract: Abstract.In this article, we determine certain conditions under which the partial sums of the multiplier integral operators of analytic univalent functions of bounded turning are also of bounded turning.Mathematical subject classification: 30C45.

Cited by 14 publications

References 9 publications

Univalent Functions Formulated by the Salagean-Difference Operator

Univalent Functions Formulated by the Salagean-Difference Operator

New Subclasses concerning Some Analytic and Univalent Functions

Upper Bound of Partial Sums Determined by Matrix Theory

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