A Subclass of Harmonic Univalent Functions Associated with -Analogue of Dziok-Srivastava Operator

By H. Aldweby, Maslina Darus. 2013

70 citations recorded by the source corpus.

We study a class of complex-valued harmonic univalent functions using a generalized operator involving basic hypergeometric function. Precisely, we give a necessary and sufficient coefficient condition for functions in this class. Distortion bounds, extreme points, and neighborhood of such functions are also considered.

Subfields: Applied Mathematics, Geometry and Topology, Polymers and Plastics

View Paper: https://www.semanticscholar.org/paper/eb36fdbe18a1ecf1caec2081459389fb29bfc876

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

In Polymers and Plastics

Citations in the corpus

Coefficient estimates of new classes of q-starlike and q-convex functions of complex order (2016, unknown): “1) belongs to the class Sq,b (φ) , then ∣∣a3− μa22∣∣ |B1b| [3]q −1 max { 1; ∣∣∣∣B2 B1 + B1b [2]q−1 ( 1− [3]q−1 [2]q−1 μ ∣∣∣∣ } .”
Some Coefficient Inequalities of q-Starlike Functions Associated with Conic Domain Defined by q-Derivative (2018, methodology): “[2] H. Aldweby and M. Darus, “A subclass of harmonic univalent functions associatedwith q-analogue of Dziok-Serivastva operator,” ISRN Mathematical Analysis, vol. 2013, Article ID 382312, 6 pages, 2013.”
Some Applications of a New Integral Operator in q-Analog for Multivalent Functions (2019, background): “For more details on the q-analog of differential and integral operators, see [17,26,27].”
Some Subordination Results on -Analogue of Ruscheweyh Differential Operator (2014, background): “Very recently, other q-analogues of differential operators have been introduced in [9]; see also ([10, 11]).”
Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator (2018, methodology): “Moreover, in recent years, such q-calculus operators as the fractional q-integral and fractional q-derivative operators were used to construct several subclasses of analytic functions (see, for example, [1], [6], [26], [27], [33], [35], [36], [37] and [38]).”
Convolution Properties for Certain Classes of Analytic Functions Defined by -Derivative Operator (2014, background): “These q-operators are defined by using convolution of normalized analytic functions and q-hypergeometric functions, where several interesting results are obtained (see also [10, 11]).”