Subordination Properties of Meromorphic Kummer Function Correlated with Hurwitz–Lerch Zeta-Function

Abstract

Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Function Theory (SPFT), are significant in developing and providing further new studies. In complex domain, the convolution tool is a salutary technique for systematic analytical characterization of geometric functions. The analytic functions in the punctured unit disk are the so-called meromorphic functions. In this present analysis, a new convolution complex operator defined on meromorphic functions related with the Hurwitz-Lerch Zeta type functions and Kummer functions is considered. Certain sufficient stipulations are stated for several formulas of this defining operator to attain subordination. Indeed, these outcomes are an extension of known outcomes of starlikeness, convexity, and close to convexity.

Geometrical Theory of Analytic Functions

“…In the analysis conducted by Firas Ghanim, Khalifa Al-Shaqsi, Maslina Darus, and Hiba Fawzi Al-Janaby in [14], a new convolution complex operator defined for meromorphic functions, related to the Hurwitz-Lerch-Zeta-type functions and Kummer functions, is considered. The Hurwitz-Lerch Zeta type functions, as part of special function theory, are significant for the development and provision of further new studies.…”

Convexity Properties for Integro‑Differential Operators Proposed by Hurwitz-Lerch Zeta Type Functions

“…al [11], Elhaddad and Darus [12], Yan and Liu [13], Oros [14], Ghanim et. al [15], Layth et. al [16] and Mahmood et.…”

Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator

“…In addition, sandwich outcomes were also yielded. This theory is very significant, and several complex analysts have contributed outstandingly to investigating the connected problems, such as Ibrahim et al [8], Srivastava et al [9], Tang et al [10], Ghanim et al [11,12], Al-Janaby et al [13], Lupas and Oros [14], Morais and Zayed [15], Attiya et al [16], Ghanim et al [17], Mishra and Gochhayat [18], and others.…”