On the Upper Bound of the Third Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function

Breaz, Daniel; Cătaş, Adriana; Cotîrlǎ, Luminiţa-Ioana

doi:10.2478/auom-2022-0005

Cited by 15 publications

(9 citation statements)

References 21 publications

(19 reference statements)

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“…This operator was previously used for obtaining differential subordination and fuzzy differential subordination results, and it is used now for introducing and studying a new subclass of functions given in Definition 4. The interesting coefficient estimates obtained in Section 3 of this paper regarding functions from this class could inspire future investigations for studying the Fekete-Szegö problem related to this class, as seen in some very recent papers, [26,27] or a certain order Hankel determinant as done in [28,29]. In Section 4, distortion properties are obtained for the functions from this class and for the derivatives which, connected to the results regarding starlikeness, convexity, and close-to-convexity shown in Section 7, could inspire future studies concerning the geometrical properties of the new subclass of functions.…”

Section: Discussionmentioning

confidence: 70%

Properties of a Subclass of Analytic Functions Defined by Using an Atangana–Baleanu Fractional Integral Operator

Lupaş

Cătaş

2022

Symmetry

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The Atangana–Baleanu fractional integral and multiplier transformations are two functions successfully used separately in many recently published studies. They were previously combined and the resulting function was applied for obtaining interesting new results concerning the theories of differential subordination and fuzzy differential subordination. In the present investigation, a new approach is taken by using the operator previously introduced by applying the Atangana–Baleanu fractional integral to a multiplier transformation for introducing a new subclass of analytic functions. Using the methods familiar to geometric function theory, certain geometrical properties of the newly introduced class are obtained such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity, and close-to-convexity of functions belonging to the class. This class may have symmetric or assymetric properties. The results could prove interesting for future studies due to the new applications of the operator and because the univalence properties of the new subclass of functions could inspire further investigations having it as the main focus.

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Section: Discussionmentioning

confidence: 70%

Properties of a Subclass of Analytic Functions Defined by Using an Atangana–Baleanu Fractional Integral Operator

Lupaş

Cătaş

2022

Symmetry

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“…The new results presented in this paper are interesting for researchers since the coefficient estimates obtained in this work could be used in the future to investigate the Fekete-Szegö relation as well as the Hankel determinants for the newly introduced classes as seen in the previously cited papers [33,34], among others.…”

Section: Discussionmentioning

confidence: 74%

Bi-Univalent Problems Involving Certain New Subclasses of Generalized Multiplier Transform on Analytic Functions Associated with Modified Sigmoid Function

2022

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The object of the present work is to investigate certain new classes of bi-univalent functions introduced in this paper using the concept of subordination. The research involves a generalized multiplier transform defined in this paper which is a generalization of known operators and the modified sigmoid function. The results contained in the proved theorems refer to coefficient estimates for the functions in the newly introduced classes.

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“…Many authors obtained coefficient estimates of bi-univalent functions in the articles [2,[14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

The Study of the New Classes of m-Fold Symmetric bi-Univalent Functions

Breaz

Cotîrlǎ

2021

Mathematics

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In this paper, we introduce three new subclasses of m-fold symmetric holomorphic functions in the open unit disk U, where the functions f and f−1 are m-fold symmetric holomorphic functions in the open unit disk. We denote these classes of functions by FSΣ,mp,q,s(d), FSΣ,mp,q,s(e) and FSΣ,mp,q,s,h,r. As the Fekete-Szegö problem for different classes of functions is a topic of great interest, we study the Fekete-Szegö functional and we obtain estimates on coefficients for the new function classes.

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On the Upper Bound of the Third Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function

Cited by 15 publications

References 21 publications

Properties of a Subclass of Analytic Functions Defined by Using an Atangana–Baleanu Fractional Integral Operator

Properties of a Subclass of Analytic Functions Defined by Using an Atangana–Baleanu Fractional Integral Operator

Bi-Univalent Problems Involving Certain New Subclasses of Generalized Multiplier Transform on Analytic Functions Associated with Modified Sigmoid Function

The Study of the New Classes of m-Fold Symmetric bi-Univalent Functions

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