Convex subclass of harmonic starlike functions

A New Subclass of Starlike Harmonic Functions Defined by Subordination

“…Recently, Öztürk et al [7], studied a family of complex valued harmonic starlike univalent functions related to uniformly convex analytic functions, denoted by * ( , [8], Jahangiri [6], Yalçın [10].…”

“…We say that an analytic function f is subordinate to an analytic function g and write , fg if there exists a complex valued function w which maps E into oneself [7]), [1], [8], [6]), (iv) ** (0,1, 1)…”

Some classes of harmonic mappings with analytic part defined by subordination

“…In [1,2,10,11,21,22,25,28,29,31], many authors further investigated various subclasses of S H and obtained some important results. In [15], the authors studied the properties of a subclassS α H of S H , consisting of all univalent antianalytic perturbations of the identity in the unit disk with |b 1 | = α , and in [16], the authors studied the classS α H of all f ∈ S H , such that |b 1 | = α ∈ (0, 1) and h ∈ CV , where CV denotes the well-known family of normalized, univalent functions that are convex.…”

“…22) and (2.24), we have: Let f = h + g be such that h and g are given by (1.2), z ∈ U. (i) If f ∈K α H (A, B), then U(0, R 1 ) ⊂ f (U), where R α)(1−ξ) 1+αξe −Aξ dξ, B = 0.…”

A new class of harmonic univalent functions by the generalized Salagean operator

“…Refs. [4][5][6][7][8][9][10][11][12][13][14][15][16] studied H S together with some geometric subclasses of H S . The differential operator n D was introduced by Salagean [17] .…”