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1

Notes on multidimensional fixed-point theorems

Akhadkulov H., Noorani S. M., Saaban A. B., Alipiah F. M., Alsamir H.

Demonstratio Mathematica

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2017

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Vol. 50, nr 1

360--374

EN

In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ ,θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

2

Partially Ordered Domains for Representing Activities

Winkowski J.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2015

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Nr 1033

1--15

EN

The paper describes structures which can be used to represent activities of broad class. The concept of event structure is generalized to represent activities which may be discrete, continuous, or of mixed nature. Configuration structures of the more general event structures are used to deńe axiomatically configuration domains. Elements of such domains are abstract representants of runs of represented activities. The partial order of elements reects how each run extends to longer runs. It is shown that configuration domains deńe event structures which can be interpreted as interactions of sets of objects.

PL

Praca opisuje struktury, których można użyć do reprezentowania szeroko rozumianych działalności. Uogólnia struktury zdarzeń tak, by mogły reprezentować działalności dyskretne, ciągłe i mieszanej natury. Konfiguracje tak uogólnionych struktur zdarzeń zostały użyte do aksjomatycznej definicji dziedzin konfiguracji. Elementy takich dziedzin są abstrakcyjnymi reprezentantami przebiegów reprezentowanych działalności. Pokazano, że dziedziny konfiguracji definiują struktury zdarzeń, które można interpretować jako współdziałania pewnych zbiorów obiektów.

3

Free algebras over a poset in varieties of Łukasiewicz-Moisil algebras

Figallo Orellano A., Gallardo C.

Demonstratio Mathematica

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2015

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Vol. 48, nr 3

348--356

EN

A general construction of the free algebra over a poset in varieties finitely generated is given in [8]. In this paper, we apply this to the varieties of Łukasiewicz–Moisil algebras, giving a detailed description of the free algebra over a finite poset (X, ≤), Free n ((X, ≤)). As a consequence of this description, the cardinality of Free n ((X, ≤)) is computed for special posets.

4

A Kannan-like contraction in partially ordered spaces

Choudhury B.S., Kundu A.

Demonstratio Mathematica

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2013

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Vol. 46, nr 2

327--334

EN

In this paper, we have introduced a generalised Kannan type contraction. It has been established that such mappings necessarily have fixed points in a complete partially ordered metric space. The fixed point is unique under some additional conditions. The result is illustrated with an example. The work is in the line of research in fixed point theory on ordered metric structures.

5

Properties of differences in B-rings

Dadej A., Halik K.

Journal of Mathematics and Applications

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2011

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Vol. 34

5-13

EN

Motivated by Pettis' extensions of Sierpinski theorems on generated families of sets, we consider B-rings, a generalization of the notion of Boolean algebras, and present their various properties. In particular, we discuss properties of differences which will be used in the proofs of results given in our forthcoming papers.