Differential superordination for harmonic complex-valued functions

Authors

  • Georgia Irina Oros University of Oradea
  • Gheorghe Oros University of Oradea

DOI:

https://doi.org/10.24193/subbmath.2019.4.04

Keywords:

Differential subordination for complex-valued harmonic functions, differential superordination for complex valued harmonic functions, subordinant, best subordinant.

Abstract

In a previously published paper,in 2015, S. Kanas introduced the differential subordination for harmonic complex-valued functions. In this article,we introduce the dual notion of differential superordination for harmonic complex-valued functions.

Author Biographies

  • Georgia Irina Oros, University of Oradea
    Department of Mathematics and Computer Science,Associate Professor
  • Gheorghe Oros, University of Oradea
    Department of Mathematics and Computer Science

References

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Lewy, H., On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Soc., 42(1936), 689-692.

Kanas, S., Differential subordinations for harmonic complex-valued functions, arxiv:1509.03751V1 [math. CV], 12 sep. 2015.

Miller, S.S., Mocanu, P.T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl., 65(1978), 298-305.

Miller, S.S., Mocanu, P.T., Differential subordinations and univalent functions, Michig. Math. J., 28(1981), 157-171.

Miller, S.S., Mocanu, P.T., Differential Subordinations, Theory and Applications, Marcel Dekker Inc., New York, Basel, 2000.

Miller, S.S., Mocanu, P.T., Subordinants of differential superordinations, Complex Variables, 48(10)(2003), 815-826.

Schaubroech, L., Subordination of planar harmonic functions, Complex Var. Theory Appl., 41(2000), 163-178.

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Published

2019-12-05

Issue

Section

Articles