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On convex and *-concave multifunctions

Bożena Piątek — 2005

Annales Polonici Mathematici

A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion 1 / ( t - s ) s t F ( x ) d x ( F ( s ) * + F ( t ) ) / 2 holds for every s,t ∈ [a,b], s < t.

On the gluing of hyperconvex metrics and diversities

Bożena Piątek — 2014

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δX) and (Y, δY ) with nonempty intersection and we wonder whether there is a natural way to glue them so that the new glued diversity (or metric space) remains being hyperconvex. We provide positive and negative answers in both situations.

Binomials transformation formulae for scaled Fibonacci numbers

Edyta HetmaniokBożena PiątekRoman Wituła — 2017

Open Mathematics

The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.

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