Fekete-Szego Inequality For Analytic And Bi-univalent Functions Subordinate To (p; q)-Lucas Polynomials

Amourah, Ala

doi:10.48550/arxiv.2004.00409

Cited by 3 publications

(3 citation statements)

References 11 publications

(12 reference statements)

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“…Hence it is obvious that such inequalities were obtained regarding bi-univalent functions too and very recently published papers can be cited to support the assertion that the topic still provides interesting results [2,6,41]. Inspiring new results emerged when quantum calculus was involved in the studies, as can be seen in many papers [30] and in studies published very recently [5,12,17,39]. Some elements of the (p, q)-calculus must be used for obtaining the original results contained in this paper.…”

Section: Srivastava Et Al In the Papermentioning

confidence: 55%

The study of coefficient estimates and Fekete–Szegö inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator

Breaz

Cotîrlǎ

2023

J Inequal Appl

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The objective of this paper is to introduce new classes of m-fold symmetric bi-univalent functions. We discuss estimates on the Taylor–Maclaurin coefficients $|a_{m+1}|$ | a m + 1 | and $|a_{2m+1}|$ | a 2 m + 1 | , and the Fekete–Szegő problem is also considered for the new classes of functions introduced. We denote these classes by $MF-S_{\Sigma ,m}^{p,q}(h)$ M F − S Σ , m p , q ( h ) , $MF-S_{\Sigma , m}^{p,q}(s)$ M F − S Σ , m p , q ( s ) , and $MF-S_{\Sigma , m}^{b,d}$ M F − S Σ , m b , d . Quantum calculus aspects are also considered in this study to enhance its novelty and to obtain more interesting results.

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Section: Srivastava Et Al In the Papermentioning

confidence: 55%

The study of coefficient estimates and Fekete–Szegö inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator

Breaz

Cotîrlǎ

2023

J Inequal Appl

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“…The Fekete-Szegö inequalities introduced in 1933, see [28], preoccupied researchers regarding different classes of univalent functions [29,30]; hence, it is obvious that such inequalities were obtained regarding bi-univalent functions too and very recently published papers can be cited to support the assertion that the topic still provides interesting results [31][32][33]. Inspiring new results emerged when quantum calculus was involved in the studies, as can be seen in many papers [34,35] and in studies published very recently [36][37][38][39][40]. Some elements of the (p; q)-calculus must be used for obtaining the original results contained in this paper.…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions

Oros

Cotîrlǎ

2022

Mathematics

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The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients |am+1| and |a2m+1| are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.

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“…This subject has attracted great interest among investigators in Geometric Function Theory. (see, for example, [4,6,16,17,21,[23][24][25][26][27][28][29][30][31]).…”

Section: Introductionmentioning

confidence: 99%

On a Fekete–Szegö Problem Associated with Generalized Telephone Numbers

et al. 2023

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One of the important problems regarding coefficients of analytical functions (i.e., Fekete–Szegö inequality) was raised by Fekete and Szegö in 1933. The results of this research are dedicated to determine upper coefficient estimates and the Fekete–Szegö problem in the class WΣ(δ,λ;ϑ), which is defined by generalized telephone numbers. We also indicate some specific conditions and consequences of results found by us.

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Fekete-Szego Inequality For Analytic And Bi-univalent Functions Subordinate To (p; q)-Lucas Polynomials

Cited by 3 publications

References 11 publications

The study of coefficient estimates and Fekete–Szegö inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator

The study of coefficient estimates and Fekete–Szegö inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator

Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions

On a Fekete–Szegö Problem Associated with Generalized Telephone Numbers

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