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1
Content available remote

Borel partitions of unity and lower Carathéodory multifunctions

100%
Srivastava S. M.
Fundamenta Mathematicae
|
1994-1995
|
tom 146
|
nr 3
239-249
EN
We prove the existence of Carathéodory selections and representations of a closed convex valued, lower Carathéodory multifunction from a set A in $A(ℰ ⊗ ℬ(X))$ into a separable Banach space Y, where ℰ is a sub-σ-field of the Borel σ-field ℬ(E) of a Polish space E, X is a Polish space and A is the Suslin operation. As applications we obtain random versions of results on extensions of continuous functions and fixed points of multifunctions. Such results are useful in the study of random differential equations and inclusions and in mathematical economics.   As a key tool we prove that if A is an analytic subset of E × X and if ${U_n : n ∈ w}$ is a sequence of Borel sets in A such that $A=∪_n U_n$ and the section $U_n(e)$ is open in A(e), e ∈ E, n ∈ w, then there exist Borel functions $p_n : A → [0,1]$, n ∈ w, such that for every e ∈ E, ${p_n(e,·) : n ∈ w}$ is a locally Lipschitz partition of unity subordinate to ${U_n(e) : n ∈ w}$.
2
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Time to the convergence of evolution in the space of population states

100%
Karcz-Dulęba I.
International Journal of Applied Mathematics and Computer Science
|
2004
|
tom 14
|
nr 3
279-287
EN
Phenotypic evolution of two-element populations with proportional selection and normally distributed mutation is considered. Trajectories of the expected location of the population in the space of population states are investigated. The expected location of the population generates a discrete dynamical system. The study of its fixed points, their stability and time to convergence is presented. Fixed points are located in the vicinity of optima and saddles. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. In this case, fixed points are also moved away from optima. The time to convergence to fixed points depends not only on the mutation rate, but also on the distance of the points from unstability. Results show that a population spends most time wandering slowly towards the optimum with mutation as the main evolution factor.
3

Coincidence point theorems in certain topological spaces

88%
Jung J., Choi Y., Kang S., Choi Y., Lee B.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1999
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tom 19
|
nr 1-2
85-101
EN
In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in F-type topological space. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.
4
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On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem

88%
Wong P.
Fundamenta Mathematicae
|
1991-1992
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tom 140
|
nr 2
191-196
EN
Let $f,g:M_1 → M_2$ be maps where $M_1$ and $M_2$ are connected triangulable oriented n-manifolds so that the set of coincidences $C_{f,g}= {x ∈ M_1 | f(x)=g(x)}$ is compact in $M_1$. We define a Nielsen equivalence relation on $C_{f,g}$ and assign the coincidence index to each Nielsen coincidence class. In this note, we show that, for n ≥ 3, if $M_2= \widetilde M_2/K$ where $\widetilde M_2$ is a connected simply connected topological group and K is a discrete subgroup then all the Nielsen coincidence classes of f and g have the same coincidence index. In particular, when $M_1$ and $M_2$ are compact, f and g are deformable to be coincidence free if the Lefschetz coincidence number L(f,g) vanishes.
5
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Corrections to "On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem" (Fund. Math. 140 (1992), 191–196)

88%
Wong P.
Fundamenta Mathematicae
|
1992
|
tom 141
|
nr 1
97-99
6
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Fuzzy fixed point results with rational type contractions in partially ordered complex-valued metric spaces

75%
Sarwar M., Humaira H., Huang H.
Commentationes Mathematicae
|
2018
|
tom 58
|
nr 1-2
EN
In this manuscript, some fixed point results for fuzzy mappings with rational type contraction in the context of a complete partially ordered complex-valued metric space are established. The derived results generalize some fixed point theorems in the existing literature. An appropriate example is given.
7
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Classes of meromorphic multivalent functions with Montel’s normalization

75%
Dziok J.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2012
|
tom 66
|
nr 2
EN
In the paper we define classes of meromorphic multivalent functions with Montel’s normalization. We investigate the coefficients estimates, distortion properties, the radius of starlikeness, subordination theorems and partial sums for the defined classes of functions. Some remarks depicting consequences of the main results are also mentioned.
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