Premium
Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics
Author(s) -
Morais João,
Zayed Hanaa M.,
Srivastava Rekha
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7486
Subject(s) - mathematics , differential operator , hypergeometric function , geometric function theory , mathematical analysis , hadamard product , convolution (computer science) , hadamard transform , riemann hypothesis , computer science , machine learning , artificial neural network
We propose third‐order differential subordination results associated with new admissible classes of multivalent functions defined in the open unit disk on the complex plane. Besides, we investigate the geometric properties of multivalent functions associated with a novel convolution operator. This is done by taking suitable linear combinations of the classical Gaussian hypergeometric function and its derivatives up to third‐order and applying the Hadamard product (or convolution) formula for power series. The complex velocity potential and the stream function of two‐dimensional potential flow problems over a circular cylinder using both sources with sink and two sources are treated by the methods developed in the present paper. We further determine the fluid flow produced by a single source and construct a univalent function so that the image of source/sink is also source/sink for a given complex potential. Finally, some plot simulations are provided to illustrate the different results of this work.