Sharp Bounds for Neuman Means by Harmonic, Arithmetic, and Contraharmonic Means

الملخص EN

We give several sharp bounds for the Neuman means N A H and N H A ( N C A and N A C ) in terms of harmonicmean H (contraharmonic mean C) or the geometric convexcombination of arithmetic mean A and harmonic mean H(contraharmonic mean C and arithmetic mean A) and present anew chain of inequalities for certain bivariate means.