Abstract
Making use of a Salagean operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. Among the results presented in this paper including the coeffcient bounds, distortion inequality, and covering property, extreme points, certain inclusion results, convolution properties, and partial sums for this generalized class of functions are discussed.
Highlights
Introduction and PreliminariesA continuous function f = u + iV is a complex-valued harmonic function in a complex domain G if both u and V are real and harmonic in G
Making use of a Salagean operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc
In 1985, Silvia [16] studied the partial sums of convex functions of order α (0 ≤ α < 1)
Summary
In 1975, Silverman [3] introduced a new class T of analytic functions of the form f(z) = z − ∑∞ n=2 |an|zn and opened up a new direction of studies in the theory of univalent functions as well as in harmonic functions with negative coefficients [4]. Uralegaddi et al [5] introduced analogous subclasses of star-like, convex functions with positive coefficients and opened up a new and interesting direction of research. Motivated by the initial work of Uralegaddi et al [5], many researchers (see [6,7,8,9]) introduced and studied various new subclasses of analytic functions with positive coefficients but analogues results on harmonic univalent.
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