Subordination Properties of the Class of Spirallike Functions Associated with the Barnes-Mittag-Leffler Function

Yıl 2025, Cilt: 25 Sayı: 3, 477 - 482, 10.06.2025

Şahsene Altınkaya

https://doi.org/10.35414/akufemubid.1511776

Öz

The applications of the Mittag-Leffler function and its generalizations in engineering, physics, biology, and other applied sciences have led to its increased recognition. In addition, numerous studies investigate the analytical properties of this function. In this study, we examine the Barnes-Mittag-Leffler function, a generalization of the Mittag-Leffler function, defined as E_(K,v)^a (z;s)=∑_(n=0)^∞▒z^n/( (Kn+v)(〖n+a)〗^s ), where z,s∈C,a,v∈C\Z_0^- and (K)>0. Further, a new subclass S_(K,v)^a (A,λ) of spirallike functions involving the Barnes-Mittag-Leffler function is defined. Subordination properties are investigated for the newly defined class, and coefficient inequalities are obtained for functions belonging to this class.

Anahtar Kelimeler

Spirallike function , subordination , convolution , Barnes-Mittag-Leffler function

Barnes-Mittag-Leffler Fonksiyonu ile İlişkili Spirallike Fonksiyonlar Sınıfının Sabordinasyon Özellikleri

Öz

Mittag-Leffler fonksiyonunun ve genelleştirmelerinin mühendislik, fizik, biyoloji ve diğer uygulamalı bilimlerdeki doğrudan kullanımları daha fazla tanınmasını sağlamıştır. Bunun yanı sıra bu fonksiyonun analitik özelliklerinin araştırılmasına yönelik de birçok araştırma mevcuttur. Bu çalışmada, Barnes-Mittag-Leffler fonksiyonunu, Mittag-Leffler fonksiyonun bir genelleştirmesi, E_(K,v)^a (z;s)=∑_(n=0)^∞▒z^n/( (Kn+v)(〖n+a)〗^s ) (z,s∈C,a,v∈C\Z_0^- ve (K)>0) araştırılmıştır. Ayrıca, Barnes-Mittag-Leffler fonksiyonunu içeren spirallike fonksiyonlar sınıfının yeni bir alt sınıfı S_(K,v)^a (A,λ) tanımlanmıştır. Tanımlanan S_(K,v)^a (A,λ) sınıfı için sabordinasyon özellikleri incelenmiştir ve bu sınıfa ait fonksiyonlar için katsayı eşitsizlikleri elde edilmiştir.

Anahtar Kelimeler

Spirallike fonksiyon , sabordinasyon , konvolüsyon , Barnes-Mittag-Leffler Fonksiyonu

Kaynakça

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