Study of certain subclasses of analytic functions involving convolution operator

Shihab

2022

J. Phys.: Conf. Ser.

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The 𝛶 subclasses S*(τ, λ) and C*(τ, λ), as well as the class of analytic and univalent functions of the form h ( w ) = w − ∑ i = 2 ∞ | e i | w i , were studied. Sharp coefficients, distortion, as well as a function expression formula in S*(τ, λ) are determined, as well as expression formulae for functions in C*(τ, λ). In addition, convex linear combination over arithmetic average, the classes S*(τ, λ) and C*(τ, λ) are proved to be closed.

Section: Introductionsupporting

confidence: 50%

Some Classes of Univalent Function with Negative Coefficients

Shihab

2022

J. Phys.: Conf. Ser.

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“…Furthermore, if the function ℎ is univalent in 𝑈, then we get the following equivalence ℎ(𝑤) ≺ 𝑘(𝑤) is obtained if and only if ℎ(0) = 𝑘(0) and ℎ(𝑈) ⊂ 𝑘(𝑈) , this can be shown in [2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 90%

Several Subclasses of r-Fold Symmetric Bi-Univalent Functions possess Coefficient Bounds

Iraqi Journal of Science

Shihab²

2022

“…The versatile applications of the -derivative operator make it exceptionally important in the study of Geometric Function Theory. Ismail et al [18,19] proposed the concept of a -extension of the class of starlike functions for the first time in 1990. In [20], Srivastava, on the other hand, used the -calculus principles in his work, which was published by systematically employing simple (or ) hypergeometric functions:…”

Section: Definition (11):[1415] Letmentioning

confidence: 99%

A certain Subclass of Meromorphically Multivalent Q-Starlike Functions Involving Higher-Order Q-Derivatives

Ali

Shihab

2022

eijs

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The authors introduced and addressed several new subclasses of the family of meromorphically multivalent -star-like functions in the punctured unit disk in this study, which makes use of several higher order -derivatives. Many fascinating properties and characteristics are extracted systematically for each of these newly identified function classes. Distortion theorems and radius problems are among these characteristics and functions. A number of coefficient inequalities for functions belonging to the subclasses are studied, and discussed, as well as a suitable condition for them is set. The numerous results are presented in this study and the previous works on this subject are also connected together in this study.