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- Title
Properties of a Linear Operator Involving Lambert Series and Rabotnov Function.
- Authors
Salah, Jamal
- Abstract
This work is an attempt to apply Lambert series in the theory of univalent functions. We first consider the Hadamard product of Rabotnov function and Lambert series with coefficients derived from the arithmetic function σ n to introduce a normalized linear operator J R α , β z . We then acquire sufficient conditions for J R α , β z to be univalent, starlike and convex, respectively. Furthermore, we discuss the inclusion results in some special classes, namely, spiral-like and convex spiral-like subclasses. In addition, we extend the findings by incorporating two Robin's inequalities, one of which is analogous to the Riemann hypothesis.
- Subjects
LINEAR operators; RIEMANN hypothesis; ARITHMETIC functions; STAR-like functions; UNIVALENT functions
- Publication
International Journal of Mathematics & Mathematical Sciences, 2024, Vol 2024, p1
- ISSN
0161-1712
- Publication type
Article
- DOI
10.1155/2024/3657721