Brennan’s conjecture in univalent function theory states that if τ is any analytic univalent transform of the open unit disk D onto a simply connected domain G and −1/3 < p < 1, then 1/(τ ′)p belongs to the Hilbert Bergman space of all analytic square integrable functions with respect to the area measure. We introduce a class of analytic function spaces La(μp) on G and prove that Brennan’s conj...

This paper aims to introduce a measure of the non-univalency harmonic mapping. By using it, we find best approximation an analytic function by univalent

the rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. the rational bi-cubic function involves six parameters in each rectangular patch. data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

In the real world, there are many applications that find Pascal distribution to be a useful and relevant model. One of these is normal distribution. this work, we develop new subclass analytic bi-univalent functions by making use q-Pascal series as construction. These involve q-Gegenbauer polynomials, them establish our subclass. Moreover, solve Fekete–Szegö functional problem analyze various d...