In the past few years, many scholars gave much attention to use of q-calculus in geometric functions theory, and they defined new subclasses analytic harmonic functions. While using symmetric function very little work has been published so far. this research, with help fundamental concepts q-Salagean differential operator for functions, we define a class connected Janowski SH0˜m,q,A,B. First, i...

In recent years, the study of Hankel determinants for various subclasses normalised univalent functions f∈S given by f(z)=z+∑n=2∞anzn D={z∈C:|z|<1} has produced many interesting results. The main focus interest been estimating second determinant form H2,2(f)=a2a4−a32. A non-sharp bound H2,2(f) when f∈K(α), α∈[0,1) consisting convex order α was found Krishna and Ramreddy (Hankel starlike alpha. ...

Many authors have obtained some inclusion properties of certain subclasses univalent and functions associated with distribution series, such as Pascal distribution, Binomial Poisson Mittag–Leffler-type Geometric distribution. In the present paper, we obtain relations harmonic class H(α,δ) classes SH* starlike KH convex functions, also for TNHβ TRHβ operator Υ defined by applying convolution reg...

In current manuscript, using Laguerre polynomials and (p−q)-Wanas operator, we identify upper bounds a2 a3 which are first two Taylor-Maclaurin coefficients for a specific bi-univalent functions classes W∑(η,δ,λ,σ,θ,α,β,p,q;h) K∑(ξ,ρ,σ,θ,α,β,p,q;h) cover the convex starlike functions. Also, discuss Fekete-Szegö type inequality defined class.

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...

I. M. Milin proposed, in his 1971 paper, a system of inequalities for the logarithmic coefficients normalized univalent functions on unit disk complex plane. This is known as conjecture and implies Robertson which turn Bieberbach conjecture. In 1984, Louis de Branges settled long-standing by showing Recently, O. Roth proved an interesting sharp inequality based proof Branges. this following Rot...

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