Abstract
The purpose of the present paper is to obtain some inclusion relation between various subclasses of harmonic univalent functions by applying certain convolution operators associated with Wright’s generalized hypergeometric functions.
Highlights
A continuous complex-valued function f = u + iv defined in a connected domain D is said to be harmonic in D if both u and v are real harmonic in D
GðzÞ = 〠 gnzn, ∣g1∣ < 1, n=1 are analytic in the open unit disk U: They proved that the function f = h + g ∈ SH is locally univalent and sensepreserving in U, if and only if jh′ðzÞj > jg′ðzÞj, ∀ z ∈ U: For more basic studies, one may refer to Duren [2] and Ahuja [3]
SH reduces to the familiar class S of analytic functions
Summary
SH reduces to the familiar class S of analytic functions. We suppose consisting of function f ∈ SH of the form (1) with g1 = 0: we let A function f = h + g of the form (1) is said to be in the class N H ðγÞ, if it satisfy the condition A function f = h + g of the form (1) is said to be in the class GHðγÞ, if it satisfy the condition
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