Version 1
: Received: 10 December 2023 / Approved: 11 December 2023 / Online: 11 December 2023 (12:16:12 CET)
How to cite:
Salah, J. Geometric Properties of a Linear Operator Involving Lambert Series and Rabotnov Function. Preprints2023, 2023120676. https://doi.org/10.20944/preprints202312.0676.v1
Salah, J. Geometric Properties of a Linear Operator Involving Lambert Series and Rabotnov Function. Preprints 2023, 2023120676. https://doi.org/10.20944/preprints202312.0676.v1
Salah, J. Geometric Properties of a Linear Operator Involving Lambert Series and Rabotnov Function. Preprints2023, 2023120676. https://doi.org/10.20944/preprints202312.0676.v1
APA Style
Salah, J. (2023). Geometric Properties of a Linear Operator Involving Lambert Series and Rabotnov Function. Preprints. https://doi.org/10.20944/preprints202312.0676.v1
Chicago/Turabian Style
Salah, J. 2023 "Geometric Properties of a Linear Operator Involving Lambert Series and Rabotnov Function" Preprints. https://doi.org/10.20944/preprints202312.0676.v1
Abstract
In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.
Keywords
Univalent; Starlike; Convex; Hadamard product; Lambert series; Sum of divisors function; Robin’s inequalities; Riemann hypothesis; Rabotnov function
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
