Admissible Classes of Multivalent Meromorphic Functions Defined by a Linear Operator

Ekram E. Ali, Rabha M. El-Ashwah, Abeer M. Albalahi and Nicoleta Breaz ()
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Ekram E. Ali: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Rabha M. El-Ashwah: Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
Abeer M. Albalahi: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Nicoleta Breaz: Department of Mathematics, Faculty of Computer Science and Engineering, “1 Decembrie 1918” University of Alba Iulia, Street Nicolae Iorga 11-13, R-510009 Alba Iulia, Romania

Mathematics, 2022, vol. 10, issue 21, 1-12

Abstract: The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on differential subordination, one of the newest techniques used in the field, also known as the technique of admissible functions. For that, the appropriate classes of admissible functions are first defined. Based on these classes, we obtain some differential subordination and superordination results for multivalent meromorphic functions, analytic in the punctured unit disc, related to a linear operator ℑ ρ , τ p ( ν ) , for τ > 0 , ν , ρ ∈ C , such that R e ( ρ − ν ) ≧ 0 , R e ( ν ) > τ p , ( p ∈ N ) . Moreover, taking into account both subordination and superordination results, we derive a sandwich-type theorem. The connection with some other known results and an example are also provided.

Keywords: analytic function; meromorphic univalent function; differential subordination; differential superordination; sandwich-type; admissible class; linear operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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