Let be the class of analytic functions in the unit disk that are normalized with f (0)= f ′(0)− 1 = 0 and let −1 ≤ B < A ≤ 1. In this paper we study the class Gλ,α = { f ∈ : |(1− α + αz f (z)/ f ′(z))/z f ′(z)/ f (z)− (1− α)| < λ, z ∈ }, 0 ≤ α ≤ 1, and give sharp sufficient conditions that embed it into the classes S∗[A,B] = { f ∈ : z f ′(z)/ f (z) ≺ (1 +Az)/(1 + Bz)} and K(δ) = { f ∈ : 1 + z f...

Let E be a compact set in C with connected complement and positive logarithmic capacity. For any f continuous on E and analytic in the interior of E, we consider the distribution of extreme points of the error of best uniform polynomial approximation on E. Let Λ = (nj) be a subsequence of N such that nj+1/nj → 1. If, for n ∈ Λ, An(f) ⊆ ∂E denotes the set of extreme points of the error function,...

In 1999, for (0≤k&lt;∞), the concept of conic domain by defining k-uniform convex functions were introduced Kanas and Wisniowska then in 2000, they defined related k-starlike denoted k−UCV k−ST respectively. Motivated their studies, our work, we define class k-parabolic starlike functions, k−SHm,q, using quasi-subordination m-fold symmetric analytic making use Ωk. We determine coefficient bound...

In this study, by using the concepts of subordination, we define a new family RM,N,λ,γ starlike functions complex order γ connected with cardioid domain. The main contribution article consists derivations sharp inequality, considering belonging to in U. Particularly, bounds first two Taylor–Maclaurin coefficients, estimates Fekete–Szegö-type functionals, and coefficient inequalities are investi...

The quantum (or q -) calculus is widely applied in various operators which include the id="M3"> -difference ( id="M4"> -derivative) operator, and this operator plays an important role geometric function theory (GFT) as well of hypergeometric series. In our present investigation, we introduce study id="M5"> -differential ...