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  1. 16 Demonstratio Mathematica
  2. 6 Bulletin of the Polish Academy of Sciences. Mathematics
  3. 4 Opuscula Mathematica
  4. 2 Control and Cybernetics
  5. 2 Fasciculi Mathematici
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  1. 3 Górnicki J.
  2. 3 Górniewicz L.
  3. 3 Pupka K.
  4. 2 Akkouchi M.
  5. 2 Jamka M.
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  1. 2 2022
  2. 1 2020
  3. 1 2019
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  5. 1 2017
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1
Content available remote Existence results for ABC-fractional BVP via new fixed point results of F-Lipschitzian mappings
Mehmood Nayyar, Khan Israr Ali, Nawaz Muhammad Ayyaz, Ahmad Niaz
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
452--469
EN
In this article, fixed point results for self-mappings in the setting of two metrics satisfying F -lipschitzian conditions of rational-type are proved, where F is considered as a semi-Wardowski function with constant τ∈R instead of τ>0 . Two metrics have been considered, one as an incomplete while the other is orbitally complete. The mapping is taken to be orbitally continuous from one metric to another. Some examples are provided to validate our results. For applications, we present existence results for the solutions of a new type of ABC-fractional boundary value problem.
2
Content available remote A study of a meromorphic perturbation of the sine family
Domínguez Patricia, Vázquez Josué
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
8--27
EN
We study the dynamics of a meromorphic perturbation of the family λsinz by adding a pole at zero and a parameter μ , that is, fλ,μ(z)=λsinz+μ/z , where λ,μ∈C⧹{0} . We study some geometrical properties of fλ,μ and prove that the imaginary axis is invariant under fn and belongs to the Julia set when ∣λ∣≥1 . We give a set of parameters (λ,μ) , such that the Fatou set of fλ,μ has two super-attracting domains. If λ=1 and μ∈(0,2) , the Fatou set of f1,μ has two attracting domains. Also, we give parameters λ,μ such that ±π/2 are fixed points of fλ,μ and the Fatou set of fλ,μ contains attracting domains, parabolic domains, and Siegel discs, we present examples of these domains. This paper closes with an example of fλ,μ , where the Fatou set contains two types of domains, for λ,μ given.
3
Content available remote Normal structure in modulated topological vector spaces
Kozlowski Wojciech M.
Commentationes Mathematicae
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2020
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Vol. 60, No. 1/2
1--11
EN
Following the author’s recent paper On modulated topological vector spaces and applications, Bull. Aust. Math. Soc. (2020), we discuss a notion of modulated topological vector spaces, that generalise, among others, Banach spaces and modular function spaces. The interest in modulars reflects the fact that the notions of “norm like” but “non-euclidean” (i.e., possibly without the triangle property and non-necessarily homogenous) constructs to measure a level of proximity between complex objects have been used extensively in statistics and applied in many empirical scientific projects requiring an objective differentiation between several classes of objects, efficiently applied in many modern clustering and Artificial Intelligence (AI) related computer algorithms. As an example of application, we prove some results, which extend fixed point theorems from the above mentioned paper, by moving from the setting of admissible sets to a simpler and more general setup, which covers also closed bounded sets. The theory of modulated topological vector spaces provides a very minimalistic framework, where powerful geometrical, fixed point, approximation and optimisation theorems are valid under a bare minimum of assumptions.
4
Content available Difference equations with impulses
Danca Marius, Feckan Michal, Pospisil Michal
Opuscula Mathematica
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2019
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Vol. 39, no. 1
5--22
EN
Difference equations with impulses are studied focussing on the existence of periodic or bounded orbits, asymptotic behavior and chaos. So impulses are used to control the dynamics of the autonomous difference equations. A model of supply and demand is also considered when Li-Yorke chaos is shown among others.
5
Content available Metoda ortogonalna pomiaru przemieszczeń szyn w diagnostyce toru bezstykowego
Jamka M., Stoliński M., Lisowski S.
Zeszyty Naukowo-Techniczne Stowarzyszenia Inżynierów i Techników Komunikacji w Krakowie. Seria: Materiały Konferencyjne
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2018
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Nr 1(115)
47--58
PL
Lokalne przemieszczenia wzdłużne szyn, mogą zaburzyć stabilności temperatury neutralnej w szynach toru bezstykowego. Pomiar przemieszczeń oznaczonych na szynie punktów bazowych w stosunku do punktów stałych, jest obecnie jedyną metodą stosowaną na sieci PKP, która pozwala na okresową kontrolę temperatury neutralnej. W artykule przedstawione zostanie nowe urządzenie i metoda pomiaru przemieszczeń punktów bazowych w stosunku do punktów stałych w aspekcie współczesnych technologii prowadzenia pomiarów przemieszczeń.
EN
Local longitudinal displacement of the rails may disturb the stability of the neutral temperature in the contactless rails. The measurement of displacements of the base points marked on rail in relation to fixed points is currently the only one method used on the PKP network, which allows for periodic control of the neutral temperature. A new device and a method for measuring displacements of base points in relation to fixed points in the aspect of modern technologies for conducting displacement measurements have been presented in the paper.
6
Content available remote On Fixed Points of the Burrows-Wheeler Transform
Mantaci S., Restivo A., Rosone G., Russo F., Sciortino M.
Fundamenta Informaticae
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2017
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Vol. 154, nr 1/4
277--288
EN
The Burrows-Wheeler Transform is a well known transformation widely used in Data Compression: important competitive compression software, such as Bzip (cf. [1]) and Szip (cf. [2]) and some indexing software, like the FM-index (cf. [3]), are deeply based on the Burrows Wheeler Transform. The main advantage of using BWT for data compression consists in its feature of “clustering” together equal characters. In this paper we show the existence of fixed points of BWT, i.e., words on which BWT has no effect. We show a characterization of the permutations associated to BWT of fixed points and we give the explicit form of fixed points on a binary ordered alphabet {a, b} having at most four b’s and those having at most four a’s.
7
Content available Pomiary przemieszczeń szyn w strefie centralnej toru bezstykowego
Jamka M., Lisowski S.
Zeszyty Naukowo-Techniczne Stowarzyszenia Inżynierów i Techników Komunikacji w Krakowie. Seria: Materiały Konferencyjne
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2016
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Nr 2(109)
79--87
PL
Stabilności temperatury neutralnej w szynach toru bezstykowego na sieci PKP do chwili obecnej kontroluje się na podstawie pomiarów przemieszczeń oznaczonych na szynie punktów bazowych, względem ustalonego przekroju kontrolnego. W artykule przedstawiony zostanie nowy sposób i urządzenie do pomiaru przemieszczeń punktów bazowych w stosunku do punktów stałych.
EN
Stability of neutral temperature at contactless rail track of PKP network, up to now, is monitored based on the measurement of displacements of basis points marked on a rail relative to the fixed control section. A new method and an apparatus for measuring the displacement of basis points relative to the fixed points has been presented in the paper.
8
Content available Integral and fractional equations, positive solutions, and Schaefer’s fixed point theorem
Becker L. C., Burton T. A., Purnaras I. K.
Opuscula Mathematica
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2016
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Vol. 36, no. 4
431--458
EN
This is the continuation of four earlier studies of a scalar fractional differential equation of Riemann-Liouville type [formula] in which we first invert it as a Volterra integral equation [formula] and then transform it into [formula] where R is completely monotone with [formula] and J is an arbitrary positive constant. Notice that when x is restricted to a bounded set, then by choosing J large enough, we can frequently change the sign of the integrand in going from (b) to (c). Moreover, the same kind of transformation will produce a similar effect in a wide variety of integral equations from applied mathematics. Because of that change in sign, we can obtain an a priori upper bound on solutions of (b) with a parameter λ ∈ (0, 1] and then obtain an a priori lower bound on solutions of (c). Using this property and Schaefer’s fixed point theorem, we obtain positive solutions of an array of fractional differential equations of both Caputo and Riemann-Liouville type as well as problems from turbulence, heat transfer, and equations of logistic growth. Very simple results establishing global existence and uniqueness of solutions are also obtained in the same way.
9
Content available remote Probabilistic generalized metric spaces and nonlinear contractions
Mbarki A., Naciri R.
Demonstratio Mathematica
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2016
|
Vol. 49, nr 4
437--452
EN
We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.
10
Content available remote L*-operators of convexity
Kulpa W.
Mathematica Applicanda
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2015
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Vol. 43, No. 2
145--156
EN
A notion of L^*-spaces is investigated as a generalization of convex subspaces. This gives some topological extensions for celebrated theorems due to Maynard Smith, Brouwer and Nash.
PL
W pracy jest badane pojęcie uogólnionej wypukłości, które umożliwia otrzymanie bardzo prostych dowodów twierdzenia Maynarda Smitha o istnieniu strategii ewolucyjnych w modelach biologicznych oraz twierdzenia o sygnaturach dających znaczne rozszerzenia twierdzenia Nasha o równowadze.
11
Content available remote Ergodicity of the Martyna-Klein-Tuckerman Thermostat and the 2014 Ian Snook Prize
Hoover W. G., Hoover C. G.
Computational Methods in Science and Technology
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2015
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Vol. 21, No. 1
5--10
EN
Nosé and Hoover’s 1984 work showed that although Nosé and Nosé-Hoover dynamics were both consistent with Gibbs’ canonical distribution neither dynamics, when applied to the harmonic oscillator, provided Gibbs’ Gaussian distribution. Further investigations indicated that two independent thermostat variables are necessary, and often sufficient, to generate Gibbs’ canonical distribution for an oscillator. Three successful time-reversible and deterministic sets of twothermostat motion equations were developed in the 1990s. We analyze one of them here. It was developed by Martyna, Klein, and Tuckerman in 1992. Its ergodicity was called into question by Patra and Bhattacharya in 2014. This question became the subject of the 2014 Snook Prize. Here we summarize the previous work on this problem and elucidate new details of the chaotic dynamics in the neighborhood of the two fixed points. We apply six separate tests for ergodicity and conclude that the MKT equations are fully compatible with all of them, in consonance with our recent work with Clint Sprott and Puneet Patra.
12
Strong convergence theorems for the approximation of fixed points of demicontinuous pseudocontractive mappings
Chidume C. E, Shehu Y.
Journal of Applied Analysis
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2013
|
Vol. 19, nr 2
213--229
EN
In this paper, we introduce a new explicit iterative scheme for approximation of fixed points of demicontinuous pseudocontractive mappings in uniformly smooth Banach spaces and prove strong convergence of our proposed iterative scheme. Furthermore, we modify our explicit iterative scheme for approximation of zeroes of bounded demicontinuous accretive mappings in uniformly smooth Banach spaces. Our result improves, extends and unifies most of the results that have been proved for this class of mappings.
13
Content available remote The Brouwer Fixed Point Theorem for Some Set Mappings
Miklaszewski D.
Bulletin of the Polish Academy of Sciences. Mathematics
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2013
|
Vol. 61, no 2
133--140
EN
For some classes X⊂2Bn of closed subsets of the disc Bn⊂Rn we prove that every Hausdorff-continuous mapping f:X→X has a fixed point A∈X in the sense that the intersection A∩f(A) is nonempty.
14
Content available remote Fixed Points of Maps of Sets of Polyhedra into the Disc
Miklaszewski D.
Bulletin of the Polish Academy of Sciences. Mathematics
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2013
|
Vol. 61, no 3-4
263--275
EN
We prove that Platonic and some Archimedean polyhedra have the fixed point property in a non-classical sense.
15
Content available Fixed points and stability in neutral nonlinear differential equations with variable delays
Ardjouni A., Djoudi A.
Opuscula Mathematica
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2012
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Vol. 32, no. 1
5-19
EN
By means of Krasnoselskii's fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307-3315], and also those of T.A. Burton [Fixed Point Theory 4 (2003), 15-32; Dynam. Systems Appl. 11 (2002), 499-519] and B. Zhang [Nonlinear Anal. 63 (2005), e233-e242]. In the end we provide an example to illustrate our claim.
16
Content available remote A new class of multivalent analytic functions defined by the hadamard product
Dziok J.
Demonstratio Mathematica
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2011
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Vol. 44, nr 2
233-251
EN
The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for classes of functions with two fixed points. Some remarks depicting consequences of the main results are also mentioned.
17
Content available remote Well-posedness of the fixed point problem for ø-max-contractions
Akkouchi M.
Fasciculi Mathematici
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2010
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Nr 45
5-12
EN
We study the well-posedness of the fixed point problem for self-mappings of a metric space which are ø-max-contractions (see [6]).
18
Content available remote Well-posedness of fixed point problem for mappings satisfying an implicit relation
Akkouchi M., Popa V.
Demonstratio Mathematica
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2010
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Vol. 43, nr 4
923-929
EN
The notion of well-posedness of a fixed point problem has generated much interest to a several mathematicians, for example, F. S. De Blassi and J. Myjak (1989), S. Reich and A. J. Zaslavski (2001), B. K. Lahiri and P. Das (2005) and V. Popa (2006 and 2008). The aim of this paper is to prove for mappings satisfying some implicit relations in orbitally complete metric spaces, that fixed point problem is well-posed.
19
Content available remote Some fixed point theorems for mappings satisfying contractive condition of integral type on d-complete topological spaces
Altun I., Turkoglu D.
Fasciculi Mathematici
|
2009
|
Nr 42
5-15
EN
In this paper, we prove two fixed point theorems for mappings satisfying contractive condition of integral type on d-complete Hausdorff topological spaces.
20
Content available remote More maps for which F(T)=F(Tn)
Jeong G., Rhoades B.
Demonstratio Mathematica
|
2007
|
Vol. 40, nr 3
671-680
EN
We continue our investigation of situations in which the fixed point sets for maps and their iterates are the same.
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