Strongly Convex Sequences

Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 161)

Abstract

Let ω≥0 be a given number and I a subinterval of ℤ. We say that a sequence (f k ) kI is ω-midconvex if
$$f_k \leq \frac{f_{k-1}+f_{k+1}}{2}-\omega \quad \mbox{for }k-1, k, k+1 \in I. $$
We give various characterizations of ω-midconvex sequences.

We also show that in a natural way one can derive from the above definition classical notions of convexity and strong convexity for functions defined on subintervals of ℝ.

Keywords

Convex function Strongly convex function 

Mathematics Subject Classification

26B25 39B62 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Institute of Computer ScienceJagiellonian UniversityKrakówPoland
  2. 2.Institute of MathematicsUniversity of RzeszówRzeszówPoland

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