H?lder mean inequalities for the generalized gr?tzsch ring and Hersch-Pfluger distortion functions

摘要

In this paper, we study the monotonicity properties of the generalized elliptic integrals and establish two H?lder mean inequalities for the generalized Gr?tzsch ring function μ_a(r) and the generalized Hersch-Pfluger distortion function Φ_K~a (r).