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2011•Journal of Inequalities and ApplicationsOpen access

Refinements of Results about Weighted Mixed Symmetric Means and Related Cauchy Means

László Horváth, Khuram Ali Khan, Josip E. Pečarić

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Abstract

A recent refinement of the classical discrete Jensen inequality is given by Horváth and Pečarić. In this paper, the corresponding weighted mixed symmetric means and Cauchy-type means are defined. We investigate the exponential convexity of some functions, study mean value theorems, and prove the monotonicity of the introduced means.

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A recent refinement of the classical discrete Jensen inequality is given by Horváth and Pečarić. In this paper, the corresponding weighted mixed symmetric means and Cauchy-type means are defined. We investigate the exponential convexity of some functions, study mean value theorems, and prove the monotonicity of the introduced means.

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Available abstract

A recent refinement of the classical discrete Jensen inequality is given by Horváth and Pečarić. In this paper, the corresponding weighted mixed symmetric means and Cauchy-type means are defined. We investigate the exponential convexity of some functions, study mean value theorems, and prove the monotonicity of the introduced means.

Key concepts: Mathematics, Convexity, Monotonic function, Cauchy distribution, Inequality of arithmetic and geometric means, Pure mathematics, Exponential function, Jensen's inequality

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