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We study MB-representations of algebras and ideals when they are relativized to a subset, and when one considers the operations of sum and intersection for families of algebras and ideals. We observe that the algebras , 3 ≤ α ≤ w 1 , on ℝ are MB-representable under GCH. We find a class of...
In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study fixed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.
The present paper gives characterizations of radially u.s.c. convex and pseudoconvex functions f : X → ℝ defined on a convex subset X of a real linear space E in terms of first and second-order upper Dini-directional derivatives. Observing that the property f radially u.s.c. does not require...
In the paper there are given new applications of dimension reduction method (from Liczberski, Starkov, Siberian Math. J. 42: 715–730, 2001) of studing linearly invariant families of holomorphic mappings in . There also included generalizing modifications of this method.
We present new semilocal convergence theorems for Newton methods in a Banach space. Using earlier general conditions we find more precise error estimates on the distances involved using the majorant principle. Moreover we provide a better information on the location of the solution. In the...
In this paper, we give a coincidence theorem, a minimax theorem, a section theorem, an intersection theorem and two existence theorems of solutions for generalized quasi-variational inequalities in hyperconvex metric spaces.
Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders ( τ -covers). We deal with two types of combinatorial questions which arise from this study. 1. Two new cardinals introduced in the topological study are...
The existence of a positive radial solution to the Dirichlet boundary value problem for the second order elliptic equation –Δ u = f ( u , ∫ U u ), where U = B (0, R ) \ B (0, ρ ), with weak assumptions on the nonlinear term f , is proved. The method based on the Krasnosel'skii Fixed Point...
Nonlinear vector integral equations are considered. Solution estimates and solvability conditions are derived. Applications to the periodic boundary value problem are also discussed. Under some restrictions our results improve the well-known ones. The main tool in the paper is the recent...
In this paper using the critical point theory of Chang J. Math. Anal. Appl. 80: 102–129, 1981 for locally Lipschitz functionals we prove an existence theorem for noncoercive Neumann problems with discontinuous nonlinearities. We use the mountain-pass theorem to obtain a nontrivial solution.
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