RADII OF CONVEXITY ASSOCIATED WITH VARIOUS SUBCLASSES OF ANALYTIC FUNCTIONS FOR FUNCTIONS RELATED TO KAPLAN CLASSES

Year 2025, Early Access, 1 - 21

Jananı B B , Nisha Bohra , V Ravichandran

https://doi.org/10.15672/hujms.1471427

Abstract

A normalized analytic function f defined on the open unit disc D is called Ma-Minda
convex if 1 + zf′′(z)/f′(z) is subordinate to the function φ. For 0 ⩽ α ⩽ β, the Kaplan class
K(α, β) of type α and β consists of normalized analytic functions of the form p^{α}g defined on D
where p with p(0) = 1 is an analytic function taking values in the right half-plane and g is an
analytic function with g(0) = 1 satisfying Re(zg′(z)/g(z)) > (α − β)/2. For functions f with
f′ ∈ K(α, β), we obtain the radius of Ma-Minda convexity for various choices of φ. The radius of
lemniscate convexity, lune convexity, nephroid convexity, exponential convexity and several other
radius estimates are examined. The results obtained are sharp.

Keywords

univalent functions, starlike functions, convex functions, close-to-convex functions, subordination, kaplan class, radius of convexity

References

• [1] R. M. Ali, N. K. Jain and V. Ravichandran, Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, Appl. Math. Comput. 218, no. 11, 6557–6565, 2012.