A subclass of harmonic functions with negative coefficients defined by Dziok-Srivastava operator

Abstract

Abstract. Making use of the Dziok-Srivastava operator, we introduce the class R p,qof complex valued harmonic functions. We investigate the coefficient bounds, distortion inequalities , extreme points and inclusion results for this class.

Multivalent harmonic functions Involving multiplier transformation

“…The above inequality must hold for all z ∈ ∆. in particular z = r → 1 yields the required condition (13). Sharpness of the result can easily be verified for the function given by (16).…”

“…and let the function f = h + g ∈ H (m) be such that h and g are given by (12). Then f ∈ R t m [α 1 ] p,q , [γ 1 ] r,s ; β; λ, k if and only if (13) holds. The inequality ( 13) is sharp for the function given by…”

Subclasses of Harmonic Mappings Defined by Convolution

“…for some 0 ≤ < 1, 0 ≤ ≤ 1 and for all ∈ . Several authors [3][4][5][6][7][8][9][10][11][12][13][14][15][16] have investigated various subclasses of harmonic functions. In this work, we introduce a new subclass of harmonic functions defined by convolution.…”

Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator

“…By routine procedure (see [10][11][12][13]), we can easily prove the following results; hence we state the following theorems without proof for functions in V ℓ H ( , ).…”

“…Motivated by the earlier works of [11][12][13][14] on the subject of harmonic functions, in this paper an attempt has been made to study the class of functions ∈ V H associated with Salagean operator on harmonic functions. Further, we obtain a sufficient coefficient condition for functions ∈ H given by (3) and also show that this coefficient condition is necessary for functions ∈ V H , the class of harmonic functions with positive coefficients.…”