Abstract. In this paper, we present some new improvements of generalized Hölder's inequalities, and then we obtain a new refinement of Minkowski inequality. Moreover, the obtained results are used to improve Chung's inequality and Beckenbach-type inequality proposed by Wang.Mathematics subject classification (2010): 26D15, 26D10.
For a polygon V 1 ...V n in the Euclidean plane, let V 1 1 ...V 1 n denote its midpoint polygon. By induction, its m -th midpoint polygon V m 1 ...V m n is defined to be the midpoint polygon ofIn this paper, we will give different kinds of formulas of the area of V m 1 ...V m n . We will describe the limit behavior of the area as m goes to infinity, and we will determine the infimum and the supremum of the area among all convex V 1 ...V n with a fixed area. Some affine invariants derived from the area will also be discussed. (2010): 51M25, 52A38, 52A40.
Mathematics subject classification
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