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.
Highlights
Introduction and DefinitionsAnd are an open unit disc in , and the analytic functions class in , respectively. Suppose that is the subclass of of the form where
Introduction and DefinitionsLet, and are an open unit disc in, and the analytic functions class in, respectively
-solutions in is said to be meromorphic -valent in denotes the class of all analytical meromorphic -valent functions where is represented by the forms
Summary
And are an open unit disc in , and the analytic functions class in , respectively. Suppose that is the subclass of of the form where. For more details we refer to [2,3,4], while neighborhoods of such meromorphic multivalent functions with negative coefficients have been studied in [5,6,7,8,9]. In [20], Srivastava, on the other hand, used the -calculus principles in his work, which was published by systematically employing simple (or ) hypergeometric functions: For more details about the Theory of Geometric Functions (GFT), we refer to [20]. Many researchers surveyed in the aforementioned work by Srivastava [22] They have identified several convolutionary and fractional calculus -operators. Theorem (2.1): The function of the form (1.1)is in the class if it fulfills the following condition:. We have completed the evidence of Theorem (2.3)
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