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Shoshana Abramovich

Publications and source records attributed to Shoshana Abramovich.

7 recordsLinked to original sources
arXiv2025

More on deviations from Mean Value

This paper deals with more refinements of inequalities related to deviations from Mean Value involving superquadratic and uniformly convex functions.

math.FA↗
arXiv2024

On relations between some types of convex functions

In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $ϕ$-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by superquadratic functions and how to adapt the technique used to get them in order to obtain new results satisfied by uniformly convex functions and to $ϕ$-convex functions. Also, we show examples that emphasize relations between superquadracity and some other types of convex functions

math.FA↗
arXiv2024

More on Jensen functional and convexity

In this paper we prove results on the difference between a normalized Jensen functional and the sum of other normalized Jensen functionals for convex function.

math.FA↗
arXiv2011

Superquadratic functions and refinements of inequalities between averages

In this paper upper bounds are given for the successive differences $A_{n+1}-A_{n}$ and B$_{n}-B_{n-1}$ where $A_{n}=1/(n-1) \tsum_{r=1}^{n-1}f(r/n)$, $B_{n}=1/(n+1) \tsum_{r=0}^{n}f(r/n)$ and $f$ is superquadratic function. We obtain bounds for the successive differences of the more general sequence $1/c_{n}\tsum_{r=1}^{n}f(a_{r}/b_{n})$ when $f$ is superquadratic, which refine known results for convex functions. We also obtain bounds for various successive differences when $f$ is an increasing subquadratic function.

math.NA↗