1 - 10 of 13 articles
New fixed point results for a very general class of maps on hyperconvex spaces are given. Our theory relies on the fact that hyperconvex compact spaces are absolute retracts. Also maps on 𝑘-CAR sets are discussed.
A three-dimensional real nonlinear autonomous system of a concrete type is studied. The Hopf bifurcation is analyzed and the existence of a limit cycle is proved. A positively invariant set, which is globally attractive, is found using a suitable Lyapunov-like function. Corollaries for a cubic...
For an operator 𝑇 acting from an infinite-dimensional Hilbert space 𝐻 to a normed space 𝑌 we define the upper AMD-number and the lower AMD-number as the upper and the lower limit of the net ( δ (𝑇| 𝐸 )) 𝐸∈𝐹𝐷(𝐻) , with respect to the family 𝐹𝐷(𝐻) of all finite-dimensional subspaces of 𝐻. When...
An optimal decomposition formula for the norm in the Orlicz space 𝐿(log 𝐿) α is given. New proofs of some results involving 𝐿(log 𝐿) α spaces are given and the decomposition is applied to apriori estimates for elliptic partial differential equations with the right-hand side in Zygmund classes.
The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.
Let φ be a modulus function, i.e., continuous strictly increasing function on 0, ∞), such that φ (0) = 0, φ (1) = 1, and φ (𝑥+𝑦) ≤ φ (𝑥)+ φ (𝑦) for all 𝑥, 𝑦 in 0, ∞). It is the object of this paper to characterize, for any Banach space 𝑋, extreme points, exposed points, and smooth points of the...
We consider convexly independent subsets of a given infinite set of points in the plane (Euclidean space) and evaluate the cardinality of such subsets. It is demonstrated, in particular, that situations are essentially different for countable and uncountable point sets.
The solvability conditions are established for a problem of linear conjugation for analytic functions with boundary values from the Zygmund class 𝐿(ln + 𝐿) α when the conjugation coefficient is piecewise-continuous in the Hölder sense. Solutions of the problem are constructed in explicit form.
Some fixed point theorems based on an asymptotic regularity condition have been obtained, which generalize the previously well-known results.
The properties of two families of s -orthogonal polynomials, which are connected with Chebyshev polynomials of third and fourth kind, are studied. Evaluations of the remainders are given and asymptotic formulae are calculated for the corresponding hyper-Gaussian formulae used for an approximate...
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