Abstract

The concept of subordination is attributed to Lindelöf (1909), but Littlewood and Rogosinski introduced the terms and discovered the basic relations. Two of the earliest first-order differential subordinations were given in 1935 by Goluzin and in 1947 by Robinson, but it was Miller and Mocanu who worked out the problem in detail. Different types of differential subordination were considered in the early articles of the originators of this theory, and then by other mathematicians. In this paper we introduce and explore differential subordinations related to generalized Pythagorean means i.e. arithmetic, geometric and harmonic means. By transferring the obtained results to the ground of analytic functions we obtain new concepts in geometric functions theory.

Keywords: Differential subordination; Pythagorean means; generalized harmonic mean; generalized geometric mean; generalized arithmetic mean; convex function.

MSC: 30C80, 30C45

DOI: 10.57016/MV-nUEK6859

Pages:  1--9