Artykuły naukowehttp://hdl.handle.net/11089/28192020-08-03T21:03:57Z2020-08-03T21:03:57ZBest Proximity Point Theorem in Quasi-Pseudometric SpacesPlebaniak, Roberthttp://hdl.handle.net/11089/241482018-02-23T02:00:25Z2016-01-01T00:00:00ZBest Proximity Point Theorem in Quasi-Pseudometric Spaces
Plebaniak, Robert
In quasi-pseudometric spaces (not necessarily sequentially complete), we continue the research on the quasi-generalized pseudodistances. We introduce the concepts of semiquasiclosed map and contraction of Nadler type with respect to generalized pseudodistances. Next, inspired by Abkar and Gabeleh we proved new best proximity point theorem in a quasi-pseudometric space. A best proximity point theorem furnishes sufficient conditions that ascertain the existence of an optimal solution to the problem of globally minimizing the error inf{g(x, y) : γ ϵ Ͳ(x)}, and hence the existence of a consummate approximate solution to the equation Ͳ(Χ) = х.
2016-01-01T00:00:00ZGeneralized gradients on Lie algebroidsBalcerzak, BogdanPierzchalski, Antonihttp://hdl.handle.net/11089/182302018-02-01T11:20:41Z2013-01-01T00:00:00ZGeneralized gradients on Lie algebroids
Balcerzak, Bogdan; Pierzchalski, Antoni
Generalized O(n) -gradients for connections on Lie algebroids are derived.
2013-01-01T00:00:00ZVariational Methods for a Fractional Dirichlet Problem Involving Jumarie’s DerivativeKamocki, Rafałhttp://hdl.handle.net/11089/129462018-02-22T13:02:38Z2015-07-08T00:00:00ZVariational Methods for a Fractional Dirichlet Problem Involving Jumarie’s Derivative
Kamocki, Rafał
We investigate a fractional Dirichlet problem involving Jumarie’s derivative. Using some variational methods a theorem on the
existence and uniqueness of a solution to such problem is proved. In the proof of the main result we use a fractional counterpart of
the du Bois-Reymond fundamental lemma.
2015-07-08T00:00:00ZCloning by positive maps in von Neumann algebrasŁuczak, Andrzejhttp://hdl.handle.net/11089/117572018-02-01T11:19:21Z2014-06-19T00:00:00ZCloning by positive maps in von Neumann algebras
Łuczak, Andrzej
We investigate cloning in the general operator algebra framework in arbitrary
dimension assuming only positivity instead of strong positivity of the cloning
operation, generalizing thus results obtained so far under that stronger assumption.
The weaker positivity assumption turns out quite natural when considering cloning in
the general C∗-algebra framework.
2014-06-19T00:00:00Z