Estimation of the Bounds of Some Classes of Harmonic Functions with Symmetric Conjugate Points

Abstract

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means of subordination, the analytic parts of which are reciprocal starlike (or convex) functions. Further, by combining with the graph of the function, we discuss the bound of the Bloch constant and the norm of the pre-Schwarzian derivative for the classes.

Keywords

• harmonic functions
• symmetric conjugate point
• subordination
• Bloch constant
• pre-Schwarzian derivative