Sufficient and Necessary Conditions for Generalized Distribution Series on Comprehensive Subclass of Analytic Functions

Tariq Al-Hawary, Basem Frasin and Ibtisam Aldawish ()
Additional contact information
Tariq Al-Hawary: Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816, Jordan
Basem Frasin: Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq 25113, Jordan
Ibtisam Aldawish: Mathematics and Statistics Department, College of Science, IMSIU (Imam Mohammad Ibn Saud Islamic University), Riyadh 13327, Saudi Arabia

Mathematics, 2025, vol. 13, issue 12, 1-9

Abstract: In this paper, we demonstrate a relationship between a generalized distribution series and a comprehensive subclass of analytic functions. The primary aim of this study is to determine a necessary and sufficient condition for the generalized distribution series E ϕ ∗ ( ς , z ) to belong to the inclusive subclass Π η ( Q 3 , Q 2 , Q 1 , Q 0 ) . Necessary and sufficient conditions are also given for the generalized distribution series E ϕ ∗ ( ς , z ) ℏ and the integral operator J ς ϕ ( z ) to be in the inclusive subclass Π η ( Q 3 , Q 2 , Q 1 , 0 ) . Further, we provide a number of corollaries, which improve the existing ones that are available in some recent studies. The results presented here not only improve the earlier studies, but also give rise to a number of new results for particular choices of Q 3 , Q 2 , Q 1 and Q 0 .

Keywords: analytic; univalent; generalized distribution; integral operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/12/2029/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/12/2029/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:12:p:2029-:d:1682911

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().