New Subclasses of Bi-Univalent Functions based on the Fibonacci Numbers

Rossdy, Munirah; Omar, Rashidah; Soh, Shaharuddin Cik

doi:10.2478/gm-2021-0016

Cited by 2 publications

(3 citation statements)

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“…Our motivation comes from the aspiration to find numerous novel and useful applications for the new generalised operator D s,m,k 𝜆 ,𝛼 f (z) proposed by Rossdy et al (2022) . Therefore, in this paper, we found the theorems of covering, rotation, distortion, growth and the convexity radius for functions of the class N s,m,k 𝜆 ,𝛼 ( , E) of bi-univalent functions connected with the Einstein function and D s,m,k 𝜆 ,𝛼 f (z) by using the subordination method.…”

Section: Discussionmentioning

confidence: 99%

“…From there on, many academics have developed new operators and used them in numerous research topics involving GFT. They include Rossdy et al (2022) , Wanas (2019) , Yunus et al (2017) , Elhaddad andDarus (2021) , andFrasin (2020) .…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we provide some information regarding the differential operator that is applied to examine our new subclasses. According to Rossdy et al (2022) , the differential operator is defined by:…”

Section: Introductionmentioning

confidence: 99%

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Bi-Univalent Function Classes Defined by Using an Einstein Function and a New Generalised Operator

Rossdy

Omar

Soh

2023

Sci. Technol. Indones

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Let A be the class of all analytic and univalent functions f (z) = z+Σ∞k=2 akzk in the open unit disc D = {z:|z|<1 }. S then represents the classes of every function in A that is univalent in D. For every f ∈ S, there is an inverse f−1. A function f ∈ A in D is categorised as bi-univalent if f and its inverse g = f−1 are both univalent. Motivated by the generalised operator, subordination principle, and the first Einstein function, we present a new family of bi-univalent analytic functions on the open unit disc of the complex plane. The functions contained in the subclasses are used to account for the initial coefficient estimate of |a2|. In this study, we derive the results for the covering theorem, distortion theorem, rotation theorem, growth theorem, and the convexity radius for functions of the class Ns,m,kλ,α (Σ, E) of bi-univalent functions related to an Einstein function and a generalised differential operator Ds,m,kλ,α f (z). We use the elementary transformations that preserve the class Ns,m,kλ,α (Σ, E) in order to attain the intended results. The required properties

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Section: Discussionmentioning

confidence: 99%