Mathematics (Nov 2020)

Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions

  • Georgia Irina Oros

DOI
https://doi.org/10.3390/math8112041
Journal volume & issue
Vol. 8, no. 11
p. 2041

Abstract

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The theory of differential subordinations has been extended from the analytic functions to the harmonic complex-valued functions in 2015. In a recent paper published in 2019, the authors have considered the dual problem of the differential subordination for the harmonic complex-valued functions and have defined the differential superordination for harmonic complex-valued functions. Finding the best subordinant of a differential superordination is among the main purposes in this research subject. In this article, conditions for a harmonic complex-valued function p to be the best subordinant of a differential superordination for harmonic complex-valued functions are given. Examples are also provided to show how the theoretical findings can be used and also to prove the connection with the results obtained in 2015.

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