Skip to content

Ayotunde Olajide Lasode and Rasheed Olawale Ayinla, On a linear combination of q-starlike and q-convex, Eur. J. Math. Appl. 5 (2025), Article ID 12.

Full Text: PDF

Volume 5 (2025), Article ID 12

https://doi.org/10.28919/ejma.2025.5.12

Published: 07/08/2025

Abstract:

This investigation is about a set of analytic-univalent function-kind $$\mathfrak{f}(z)=z+\sum\limits_{j\geqq2}a_jz^j,\quad |z|<1$$ analytically defined in the two novel sets: $\Omega_{q,\delta}(s,t;\eta)$ and $\mho_{q,\delta}(s,t;\gamma)$. The definition of functions $\mathfrak{f}$ in set $\Omega_{q,\delta}(s,t;\eta)$ involves the generalizations of the sets of $q$-convex and $q$-starlike functions; while $\mathfrak{f}$ in set $\mho_{q,\delta}(s,t;\gamma)$ involves the generalizations of the sets of strongly-$q$-convex and strongly-$q$-starlike funtions. In addition to these, the two sets have association with the Caratheodory functions and some real parameters. It is well-known that the subsets: $q$-convex, $q$-starlike, strongly-$q$-convex, and strongly-$q$-starlike have significant, empirical and classical features in the well-known set of analytic-univalent functions. Some mathematical principles employed in the methodology are the concepts of $q$-calculus, infinite series generation, and the linear combination of some geometric expressions. Thus, the reported results for the two novel sets span through some estimates for the Fekete-Szego coefficient functionals (with real and complex parameters) and some initial coefficient bounds. Generally speaking, the two novel sets (and their results) reduce to a number of recognized sets (and their results) when values for certain parameters are altered within their declaration interval. How to Cite: Ayotunde Olajide Lasode and Rasheed Olawale Ayinla, On a linear combination of q-starlike and q-convex, Eur. J. Math. Appl. 5 (2025), Article ID 12. https://doi.org/10.28919/ejma.2025.5.12