Volume 12, Issue 1

The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let 𝐾 1 and 𝐾 2 be nonempty closed convex subsets of real Hilbert spaces 𝐻 1 and 𝐻 2 , respectively. The two-step SNVI problem considered here is as follows: find an element (𝑥*, 𝑦*) ∈ 𝐻 1 × 𝐻 2 such that (𝑔(𝑥*), 𝑔(𝑦*)) ∈ 𝐾 1 × 𝐾 2 and where 𝑆 : 𝐻 1 × 𝐻 2 → 𝐻 1 , 𝑇 : 𝐻 1 × 𝐻 2 → 𝐻 2 , 𝑔 : 𝐻 1 → 𝐻 1 and ℎ : 𝐻 2 → 𝐻 2 are nonlinear mappings.

Here, using the ideas of an old paper by S. Dineen (An. Acad. Brasil. Ci. 48: 11–12, 1976), we give large classes of pairs (𝑋, 𝐸) such that 𝑋 is an infinite-dimensional complex space very far from a Banach manifold, 𝐸 is a holomorphic vector bundle on 𝑋 and 𝐻 1 (𝑋,𝐸) is infinite-dimensional.

A sequence of matrices 𝑈 1 , 𝑈 2 , . . . , 𝑈 𝑚 is constructed, which satisfies the conditions 𝑈 𝑖 𝑈 𝑗 = – 𝑈 𝑗 𝑈 𝑖 (𝑖 ≢ 𝑗), . These matrices are used to construct representations of a Clifford algebra for special quadratic forms.

Necessary conditions and sufficient conditions for the boundedness/ compactness of weighted Hardy operators are established in generalized Lebesgue spaces 𝐿 𝑝(𝑥) .

It is proved that the two-sided ergodic maximal operator is one-to-one.

We consider an interior problem of statics of couple-stress elasticity for anisotropic nonhomogeneous media with friction taken into account and the corresponding exterior problem for homogeneous isotropic media. The question of the existence and uniqueness of weak solutions of these problems is studied when friction forces occur along the boundary of an elastic medium or on some part of this boundary.

Optimality conditions are established in terms of Lagrange–Kuhn–Tucker multipliers for multiobjective optimization problems by a scalarization technique. Throughout this note, the data are assumed to be locally Lipschitz.

We discuss some convergence and divergence properties of twodimensional (Nörlund) logarithmic means of two-dimensional Walsh–Fourier series of functions both in the uniform and in the Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function, and also the function space.

A new restriction for the multipliers of 𝐿 𝑝 (𝐑) to 𝐿 𝑝 (𝐓) has been introduced. Our results generalize the famous De Leeuw's theorem on the transference of Fourier multipliers between 𝐑 and 𝐓.

For , the estimate is derived, where and 𝑑 𝑛 are defined by a certain recurrent formula.

For invariant (quasi-invariant) σ -finite measures on an uncountable group (𝐺, ·), the behaviour of small sets with respect to the operation “·” is studied. Some classes of non-commutative groups (𝐺, ·) are discussed especially, by using a representation of the original group in the form of a direct product of its two subgroups, one of which is commutative.

We consider weighted weak type estimates for the modified Hardy–Littlewood maximal functions on a nonhomogeneous space. We use the new covering lemma by Sawano.

We prove two theorems on the uniqueness of nonlinear differential polynomials sharing 1-points which improve an earlier result of Fang and Hong.

The very nature of the so-called Postnikov invariants is carefully studied. Two functors, precisely defined, explain the exact nature of the connection between the category of topological spaces and the category of Postnikov towers. On one hand, these functors are in particular effective and lead to concrete machine computations through the general machine program Kenzo. On the other hand, the Postnikov “invariants” will be actual invariants only when an arithmetical decision problem – currently open – will be solved; it is even possible this problem is undecidable.

Abstarct The paper discusses a new class of noncommuting maps called 𝑅-subweakly commuting maps. The existence of invariant approximations for this class of maps is established. Our results extend, generalize, and improve some known results existing in the literature.

Let 𝑇𝑓 denote the 𝑔-function 𝑔(𝑓) or the area integral 𝑠(𝑓). We give a characterization of functions Φ for which where the constant 𝐶 is independent of 𝑓.

In this paper we study some algebraic properties of harmonic forms on Poisson manifolds. It is well known that in the classical case (on Riemannian manifolds) the product of harmonic forms is not harmonic. Here we describe the algebraic and analytical mechanisms explaining this fact. We also obtain a condition under which the product of de Rham cohomology classes, which includes harmonic representatives, can be represented by a harmonic form.

The majorant of Fourier series partial sums with respect to the system of functions formed by the product of 𝐿([0, 1]) space bases is considered. It is proved that in any Orlicz space wider than 𝐿(log + 𝐿) 𝑑 ([0, 1] 𝑑 ), 𝑑 ≥ 1, the set of functions with such a majorant is integrable on [0, 1] 𝑑 and has the first Baire category.

Wintner-type oscillation criteria of semilinear elliptic inequalities are obtained by using partial Riccati technique. The results presented improve the oscillation criteria due to E. S. Noussair and C.A. Swanson [Canad. J. Math. 32: 908–923, 1980].