Some sharp inequalities involving Seiffert and other means and their concise proofs

Abstract

Abstract. In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide a unified and concise proof of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic, centroidal, arithmetic, geometric, harmonic, and root-square means of two positive real numbers a and b with a = b .Mathematics subject classification (2010): Primary 26E60; Secondary 11H60, 26A48, 26D05, 33B10.

Jordan Type Inequalities for Hyperbolic Functions and Their Applications

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“…For more information on this topic, please refer to recently published papers [4,6,7,8,9,10,14,15,16,18,23,24] and cited references therein. For positive numbers a, b > 0 with a = b, let…”