Abstract
A times continuously differentiable complex-valued function in a domain is -harmonic if satisfies the -harmonic equation , where is a positive integer. By using the generalized Salagean differential operator, we introduce a class of -harmonic functions and investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points, and convex combination of the class.
Highlights
A continuous complex-valued function f = u + iV in a domain D ⊆ C is harmonic if both u and V are real harmonic in D; that is, Δu = 0 and ΔV = 0
When p = 1, we get the generalized Salagean operator for harmonic univalent functions defined by Li and Liu [14]
The main object of the paper is to introduce a class of p-harmonic functions by using the generalized Salagean operator which was defined by Li and Liu [14]
Summary
Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059 Bursa, Turkey A p times continuously differentiable complex-valued function F = u + iV in a domain D ⊆ C is p-harmonic if F satisfies the pharmonic equation Δ ⋅ ⋅ ⋅ ΔF = 0, where p is a positive integer. By using the generalized Salagean differential operator, we introduce a class of p-harmonic functions and investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points, and convex combination of the class.
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