By making use of a higher-order q-derivative operator, certain families meromorphic q-starlike functions and q-convex are introduced studied. Several sufficient conditions coefficient inequalities for in these subclasses derived. The results presented this article extend generalize number previous results.

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

The aim of this paper is two-fold. First, to give a direct proof for the already established result of Styer which states that a univalent geometrically starlike function f is a univalent annular starlike function if f is bounded. Second, to show that the boundedness condition of f is necessary, thus disproving a conjecture of Styer.

In this paper, we define a new family of q-starlike and q-convex functions related to the cardioid domain utilizing ideas subordination Sălăgean quantum differential operator. The primary contribution article is derivation sharp inequality for newly established subclasses in open unit disc U. For novel family, bounds first two Taylor–Maclaurin coefficients, Fekete–Szegö-type functional, coeffic...

are classes of starlike and strongly starlike functions of order β (0 < β ≤ 1), respectively. Note that S∗(β)⊂ S∗ for 0< β< 1 and S∗(1)= S∗ [5]. Kanas [2] introduced the subclass R̄δ(β) of function f ∈ S as the following. Definition 1.1. For δ ≥ 0, β ∈ (0,1], a function f normalized by (1.1) belongs to R̄δ(β) if, for z ∈D−{0} and Dδf(z)≠ 0, the following holds: ∣∣∣arg z ( Dδf(z) )′ Dδf(z) ∣∣∣≤ βπ...

In a recent paper [2], G. R. Blakley raised a question about the decomposition of a ^-valent starlike function into the product of two ^-valent starlike functions. It is the purpose of this note to prove the conjecture of Blakley. Definition 1. The function/(z), regular in |z| <1, is said to be in the class S(p, m), where p and m are positive integers with p^m, if and only if (1) there exists a...