Optimal bounds for Seiffert-like elliptic integral mean by harmonic, geometric, and arithmetic means

Abstract

Abstract In this article, we present the optimal bounds for a special elliptic integral mean in terms of the harmonic combinations of harmonic, geometric, and arithmetic means. As consequences, several new bounds for the complete elliptic integral of the second kind are discovered, which are the improvements of many previously known results.

Keywords

• Seiffert-like mean
• Complete elliptic integral
• Harmonic mean
• Geometric mean
• Arithmetic mean