engleski

Improvement of an extension of Holder-type inequality

In 1995 Pearce and Pečarić proved an extension of Holder-type inequality using generalization of Steffensen's inequality given by Mitrinović and Pečarić in 1988. We define functionals related to that extension and prove their n-exponential, exponential and logarithmic convexity. Moreover, we improve that extension using logarithmic convexity of defined functionals. Furthermore, we define new Cauchy-type means and prove their monotonicity property.

Holder inequality; Steffensen inequality; exponential convexity; logarithmic convexity; Cauchy means

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