Some Inequalities and Other Results Associated with Certain Subclasses of Univalent and Bi-Univalent Analytic Functions

Srivástava, H. M.

doi:10.1007/978-1-4614-3498-6_38

Cited by 22 publications

(15 citation statements)

References 32 publications

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“…Motivated by their work [13], many researchers (see, for example, [3,5,6,11,13,14,12,15,16,17,18]; see also the various closely-related papers on the subject, which are cited in some of these works) have recently investigated several interesting subclasses of the bi-univalent function class Σ and found non-sharp estimates on the first two Taylor-Maclaurin coefficients of functions belonging to these subclasses.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Initial coefficient bounds for a subclass of $m$-fold symmetric bi-univalent functions

2014

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Let Σ denote the class of functions f (z) = z + ∞ ∑ n=2 anz n belonging to the normalized analytic function class A in the open unit disk U, which are bi-univalent in U, that is, both the function f and its inverse f −1 are univalent in U. The usual method for computation of the coefficients of the inverse function= z is too difficult to apply in the case of m-fold symmetric analytic functions in U. Here, in our present investigation, we aim at overcoming this difficulty by using a general formula to compute the coefficients of f −1 (z) in conjunction with the residue calculus. As an application, we introduce two new subclasses of the bi-univalent function class Σ in which both f (z) and f −1 (z) are m-fold symmetric analytic functions with their derivatives in the class P of analytic functions with positive real part in U. For functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for |am+1| and |a2m+1|.

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Section: Introduction and Definitionsmentioning

confidence: 99%

Initial coefficient bounds for a subclass of $m$-fold symmetric bi-univalent functions

2014

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“…Properties of certain integral operators were studied by different authors in the following papers [2,16,17,18,19,20].…”

Section: Pescar a Sasu -Classes Of An Univalent Integral Operatormentioning

confidence: 99%

Classes of an Univalent Integral Operator

2017

Acta Univ. Apulensis Math. Inform.

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“…In fact, the aforecited work of Srivastava et al [18] essentially revived the investigation of various sublasses of the bi-univalent function class Σ in recent years; it was followed by such works as those by Ali et al [3], Srivastava et al [17], Jahangiri and Hamidi [8] (see also [7,14,5,13] and the references cited in each of them).…”

Section: Introductionmentioning

confidence: 95%

Coefficient estimates for a certain class of analytic and bi-univalent functions defined by fractional derivative

Akın

Eker

2014

Comptes Rendus. Mathématique

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Some Inequalities and Other Results Associated with Certain Subclasses of Univalent and Bi-Univalent Analytic Functions

Cited by 22 publications

References 32 publications

Initial coefficient bounds for a subclass of $m$-fold symmetric bi-univalent functions

Initial coefficient bounds for a subclass of $m$-fold symmetric bi-univalent functions

Classes of an Univalent Integral Operator

Coefficient estimates for a certain class of analytic and bi-univalent functions defined by fractional derivative

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