New differential operator for analytic univalent functions associated with binomial series

• Published in: AIP Conference Proceedings
• Main Author: Rossdy M.; Omar R.; Soh S.C.
• Format: Conference paper
• Language: English
• Published: American Institute of Physics Inc. 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85182580896&doi=10.1063%2f5.0171850&partnerID=40&md5=36f9c8c5e8295ecd307c99fee1046500

The investigation of operators is significant in mathematics, particularly in geometric function theory. Operators have generated a considerable amount of attention in the theory of geometric functions because of their significance in generalising and preserving subclasses of analytic univalent functions. Many mathematicians have discussed operators and the new generalisation in various articles. Research on operators has been conducted since 1915. Since then, mathematicians are still very interested in discussing operators with many properties of analytic univalent functions. Hence, this paper introduces a new generalised operator Dλ,αs,m,kf(z) of analytic functions in the open unit disc using the generalised Srivastava-Attiya operator, generalised Al-Oboudi operator, and binomial series. Based on this new operator, some subclasses are defined using differential subordinations method. Furthermore, the inclusion properties are obtained for functions in these subclasses. © 2024 Author(s).