Subordination and superordination results for analytic functions with respect to symmetrical points

Abstract

The theory of symmetric functions has many applications in the investigation of fixed points, estimation of absolute values of some integrals and obtaining the results of the type of Cartan’s uniqueness theorem. In this paper, we solve some differential subordinations and superordinations involving analytic functions with respect to the symmetric points and also derive some sandwich results under certain assumptions on the parameters involved. The various results presented in this paper are shown to apply to yield the corresponding (new or known) results for many simpler function classes.

Mathematics Subject Classification (2010):

• Primary 30C45
• Secondary 30C80

Key words:

• Analytic functions
• starlike functions
• differential subordination
• superordination and sandwich results