Abstract
For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1nηi=0f(ai/an) are also included.
Original language | English |
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Pages (from-to) | 535-550 |
Number of pages | 16 |
Journal | Mathematical Inequalities and Applications |
Volume | 19 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2016 |
Keywords
- Convexity
- Differences of averages
- Inequalities
- Lower bounds.
- Refinements
- Superquadracity
- γ-quasiconvexity
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics