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<p>In this paper we put in a new light the concept of <i>barycenter</i> for discrete Steffensen Popoviciu measures supported in some points belonging to a space with curved geometry. More precisely, we prove the existence of the <i>barycenter</i> if we relax the restrictions imposed on the weights of the measure. As applications, we deduce Jensen-Steffensen, Hardy-Littlewood-Polya and Sherman type inequalities on spaces with global nonpositive curvature, even in the case when nonpositive weights are chosen.</p>

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On the barycenter for discrete Steffensen Popoviciu measures on global NPC spaces

  • 期刊论文

  • 发表日期：

    2025年12月27日

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  • Geanina Maria Lăchescu,
  • Maria Mălin,
  • Ionel Rovenţa

摘要

In this paper we put in a new light the concept of barycenter for discrete Steffensen Popoviciu measures supported in some points belonging to a space with curved geometry. More precisely, we prove the existence of the barycenter if we relax the restrictions imposed on the weights of the measure. As applications, we deduce Jensen-Steffensen, Hardy-Littlewood-Polya and Sherman type inequalities on spaces with global nonpositive curvature, even in the case when nonpositive weights are chosen.