A Study of a Certain Family of Multivalent Functions Associated with Subordination

Rasheed, Reem O.; Jassim, Kassim A.

doi:10.24996/ijs.2021.62.9.16

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…ematicians based on subordinate techniques, for instance, Zayed and Bulboacă [39], Attiy et al [40], Lupaş and Oros [41], Reem and Kassim [42], Abdulnabi et al [43], Oros and Oros [44], Oros [45], and others. On the other hand, the study of interesting geometric attributes associated with some families of special functions has attracted a lot of investigators and experts, such as Merkes and Scott [46] in 1961, who examined starlike hypergeometric functions.…”

Section: Proposed Logarithm-hurwitz-lerch Zeta Functionmentioning

confidence: 99%

“…In other words, this principle acts as a gist tool of the holomorphic class of functions in which characterizations of functions are inferred from a differential stipulation. Recently, advanced studies have been extensively conducted by famed mathematicians based on subordinate techniques, for instance, Zayed and Bulboacă [39], Attiy et al [40], Lupaş and Oros [41], Reem and Kassim [42], Abdulnabi et al [43], Oros and Oros [44], Oros [45], and others. On the other hand, the study of interesting geometric attributes associated with some families of special functions has attracted a lot of investigators and experts, such as Merkes and Scott [46] in 1961, who examined starlike hypergeometric functions.…”

Section: Introductionmentioning

confidence: 99%

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Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method

Abdulnabi,

F. Al-Janaby,

Ghanim

et al. 2024

Symmetry

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The interest in special complex functions and their wide-ranging implementations in geometric function theory (GFT) has developed tremendously. Recently, subordination theory has been instrumentally employed for special functions to explore their geometric properties. In this effort, by using a convolutional structure, we combine the geometric series, logarithm, and Hurwitz–Lerch zeta functions to formulate a new special function, namely, the logarithm-Hurwitz–Lerch zeta function (LHL-Z function). This investigation then contributes to the study of the LHL-Z function in terms of the geometric theory of holomorphic functions, based on the differential subordination methodology, to discuss and determine the univalence and convexity conditions of the LHL-Z function. Moreover, there are other subordination and superordination connections that may be visually represented using geometric methods. Functions often exhibit symmetry when subjected to conformal mappings. The investigation of the symmetries of these mappings may provide a clearer understanding of how subordination and superordination with the Hurwitz–Lerch zeta function behave under different transformations.

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Section: Proposed Logarithm-hurwitz-lerch Zeta Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method

Abdulnabi,

F. Al-Janaby,

Ghanim

et al. 2024

Symmetry

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New Results of Differential Subordination for a Specific Subclass of p-Valent Meromorphic Functions Involving a New Operator

Shehab,

Juma,

Cotîrlă

et al. 2024

Axioms

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The present article aims to significantly improve geometric function theory by making an important contribution to p-valent meromorphic and analytic functions. It focuses on subordination, which describes the relationships of analytic functions. In order to achieve this, we utilize a technique that is based on the properties of differential subordination. This approach, which is one of the most recent developments in this field, may obtain a number of conclusions about differential subordination for p-valent meromorphic functions described by the new operator IHp,q,s j,pν1,n,α,lJ(ζ) within the porous unit disk Δ. Numerous mathematical and practical issues involving orthogonal polynomials, such as system identification, signal processing, fluid dynamics, antenna technology, and approximation theory, can benefit from the results presented in this article. The knowledge and comprehension of the unit’s analytical functions and its interacting higher relations are also greatly expanded by this text.

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A Study of a Certain Family of Multivalent Functions Associated with Subordination

Abstract: The aim of this paper is to introduce a certain family of new classes of multivalent functions associated with subordination. The various results obtained here for each of these classes include coefficient estimates radius of convexity, distortion and growth theorem.

Cited by 2 publications

References 7 publications

Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method

Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method

New Results of Differential Subordination for a Specific Subclass of p-Valent Meromorphic Functions Involving a New Operator

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