Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator

Abstract

In this article, we construct a new subclass of analytic functions involving a generalized differential operator and investigate certain properties including the radius of starlikeness, closure properties and integral means result for the class of analytic functions with negative coefficients. Further, the relationship between the results and some known results in literature are also established.

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

“…Introducing and studying new classes of univalent functions generates very interesting results and we can find only a few, very recent studies regarding this, such as new subclasses for bi-univalent functions [18,19] and classes of functions introduced using operators [20]. We have previously used fractional integrals for introducing new subclasses of functions [21], and, motivated by the interesting results obtained, we have decided to apply the operator introduced by applying the Atangana-Baleanu fractional integral to a multiplier transformation for defining a new subclass of functions.…”

Subclasses of Analytic Functions with Negative Coefficients Involving q-Derivative Operator

“…For f ∈ V , there are some signi cant researchers for example in (Halim et al, 2005) , the authors studied the class M * S V (𝜂 , 𝜗) consisting of starlike functions with respect to (w.r.t) symmetric points. Besides, there are various studies for example in (Al-Abbadi and Darus, 2010;Al Shaqsi and Darus, 2007;Atshan and Ghawi, 2012;Bucur and Breaz, 2020;Choo and Janteng, 2013;Halim et al, 2006;Janteng and Halim, 2009;Najafzadeh and Salleh, 2022;Oluwayemi et al, 2022;Porwal et al, 2022).…”