We introduce universally convex, starlike and prestarlike functions in the slit domain C \ [1,∞), and show that there exists a very close link to completely monotone sequences and Pick functions.

Inclusion relations for k−uniformly starlike functions under the Dziok-Srivastava operator are established. These results are also extended to k−uniformly convex functions, close-to-convex, and quasi-convex functions.

This paper establishes the upper bounds for second and third coefficients of holomorphic bi-univalent functions in a family which involves Bazilevic μ-pseudo-starlike under new operator, joining neutrosophic Poisson distribution with modified Caputo’s derivative operator. We also discuss Fekete–Szego’s function problem this family. Examples are given to support our case distribution. The fields...

then we say that p is the Catathéodory function. LetA denote the class of all functions f analytic in the open unit disk U {z : |z| < 1} with the usual normalization f 0 f ′ 0 − 1 0. If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f z ≺ g z , if g is univalent, f 0 g 0 and f U ⊂ g U . For 0 < α ≤ 1, let STC α and STS α denote the classes of functions f ∈ A whic...

For d > 0 let Dd = {z : |z| < d} with D1 = D and let ∂Dd denote the boundary of Dd. Let S be the standard class of analytic, univalent functions f on D, normalized by f(0) = 0 and f ′(0) = 1 and let K denote the wellknown class of convex functions in S. For 0 ≤ α < 1 let S∗(α) denote the subclass of S of starlike functions of order α, i.e., a function f ∈ S∗(α) if and only if f satisfies the co...

These are normalized functions regular and univalent in E: IzI < 1, for which f( E) is starlike with respect to the origin. Let y be a circle contained in E and let [ be the center of y. The Pinchuk question is this: Iff(z) is in ST, is it true thatf(y) is a closed curve that is starlike with respect tof(i)? In Section 5 we will see that the answer is no. There seems to be no reason to demand t...

Denote by A the class of all functions f , normalized by f(0) = f ′(0) − 1 = 0, that are analytic in the unit disk ∆ = {z ∈ C : |z| < 1}, and by S the subclass of univalent functions in ∆. Denote by S∗ the subclass consisting of functions f in S that are starlike (with respect to origin), i.e., tw ∈ f(∆) whenever t ∈ [0, 1] and w ∈ f(∆). Analytically, f ∈ S∗ if and only if Re (zf ′(z)/f(z)) > 0...

which are analytic in the open unit disk U {z : z ∈ C and |z| < 1} and S denote the subclass ofA that are univalent in U. A function f z inA is said to be in class S∗ of starlike functions of order zero in U, if R zf ′ z /f z > 0 for z ∈ U. Let K denote the class of all functions f ∈ A that are convex. Further, f is convex if and only if zf ′ z is star-like. A function f ∈ A is said to be close...