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

Abstract

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.

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

“…The function 𝑙 defined by 𝑙(𝑤) = √ℎ(𝑤 𝑟 ) 𝑟 , (𝑟 ∈ {1,2,3, … }) maps and its is univalent in 𝑈 into a place that 𝑟-fold symmetry for all ℎ ∈ ℋ. If the condition of normalized is met, a function is said to be 𝑟-fold symmetric (see [17][18][19]).…”

Certain Subclasses of Meromorphic Functions Involving Differential Operator

“…And we denote by ∑ (𝜀) * 𝑘 the class of meromorphically convex functions of 𝜀. The class ∑ * (𝜀) and ∑ (𝜀) were introduced and studied by pommerenke [1], Miller [2], Mogra et al [3], Aouf et al [4,5], El-Ashwah et al [6], Mostafa et al [7] and Venkateswarlu et al [8,9,10].…”

“…where ℑ 𝜏,𝑢,ℎ,𝑡 𝑚,𝑘 (𝑓 * 𝑔)(𝑤) is given by (9). In addition, we state that a function(𝑓 * 𝑔)(𝑤) ∈ ∑(𝛼, 𝛿, 𝒴, 𝜏, 𝑢, ℎ, 𝑡), whenever (𝑓 * 𝑔)(𝑤) is of the form (4).…”