Volume 18, Issue 1

In this paper two existence results concerning the global attractivity and global asymptotic attractivity for a certain functional nonlinear integral equation are proved. Our existence results include several existence and attractivity results obtained earlier by Darwish and Hu–Yan as special cases under weaker conditions. A fixed point theorem of Dhage is used in formulating our main results and the characterizations of solutions are obtained in the space of functions defined, continuous and bounded on unbounded intervals.

The aim of this paper is to prove the characterization on a bounded domain of with fractal boundary and a Hölder continuous function on the boundary guaranteeing the biregular extendability of the later function throughout the domain.

Let k be a positive integer, and let ℱ be a family of functions holomorphic on a domain D in C , all of whose zeros are of multiplicity at least k + 1. Let h be a function meromorphic on D , h ≢ 0, ∞. Suppose that for each ƒ ∈ ℱ, ƒ ( k ) ( z ) ≠ h ( z ) for z ∈ D . Then ℱ is a normal family on D . The condition that the zeros of functions in ℱ are of multiplicity at least k + 1 cannot be weakened, and the corresponding result for families of meromorphic functions is no longer true.

It is shown that, under certain assumptions, the functional difference equations have at least three positive periodic solutions. Applications are given to illustrate the main results.

Using a special scalarization employed for the first time for the study of necessary optimality conditions in vector optimization by Ciligot-Travain [Numer. Funct. Anal. Optim. 15: 689–693, 1994], we give necessary optimality conditions for a set-valued optimization problem by establishing the existence of Lagrange–Fritz–John multipliers. Also, sufficient optimality conditions are given without any Lipschitz assumption.

Define the two dimensional diagonal Sunouchi operator where S 2 n , 2 n ƒ and σ 2 n ƒ are the (2 n , 2 n )th cubic-partial sums and 2 n th Marcinkiewicz–Fejér means of a two-dimensional Walsh–Fourier series. The main aim of this paper is to prove that the operator is bounded from the Hardy space H 1/2 to the weak L 1/2 space and is not bounded from the Hardy space H 1/2 to the space L 1/2 .

In this paper, we introduce the notion of a screen slant lightlike submanifold of an indefinite cosymplectic manifold. We provide a characterization theorem for the existence of a screen slant lightlike submanifold with examples. Also, we give an example of a minimal screen slant lightlike submanifold of and prove some characterization theorems.

The paper is devoted to the mathematical analysis of scattered time-harmonic electromagnetic waves by an infinitely long cylindrical orthotropic waveguide iris. This is modeled by an orthotropic Maxwell system in a cylindrical waveguide iris for plane waves propagating in the x 3 -direction, imbedded in an isotropic infinite medium. The problem is equivalently reduced to a 2-dimensional boundary-contact problem with the operator div M grad+ k 2 inside the domain and the (Helmholtz) operator Δ+ k 2 = div grad+ k 2 outside the domain. Here M is a 2 × 2 positive definite, symmetric matrix with constant, real valued entries. The unique solvability of the appropriate boundary value problems is proved and the regularity of solutions is established in Bessel potential spaces.

A necessary and sufficient condition for a complete sequence of subspaces to be a fusion Banach frame for E is given. Also, we introduce fusion Banach frame sequences and give a characterization for a complete sequence of subspaces of E to be a fusion Banach frame for E in terms of fusion Banach frame sequences. Finally, along with other results, we characterize fusion Banach frames in terms of Banach frames.

We consider some Muckenhoupt type weight classes on nondoubling measure space (, μ ) and give an example of measure μ such that where α 1 ≠ α 2 .

Suppose that is an algebra, σ, τ : → are two linear mappings such that both σ () and τ () are subalgebras of and 𝒳 is a ( τ (), σ ())-bimodule. A linear mapping D : → 𝒳 is called a ( σ, τ )-derivation if D ( ab ) = D ( a ) · σ ( b ) + τ ( a ) · D ( b ) ( a, b ∈ ). A ( σ, τ )-derivation D is called a ( σ, τ )-inner derivation if there exists an x ∈ 𝒳 such that D is of the form either or . A Banach algebra is called ( σ, τ )-amenable if every ( σ, τ )-derivation from into a dual Banach ( τ (), σ ())-bimodule is ( σ, τ )-inner. Studying some general algebraic aspects of ( σ, τ )-derivations, we investigate the relation between the amenability and the ( σ, τ )-amenability of Banach algebras in the case where σ, τ are homomorphisms. We prove that if 𝔄 is a C *-algebra and σ, τ are *-homomorphisms with ker( σ ) = ker( τ ), then 𝔄 is ( σ, τ )-amenable if and only if σ (𝔄) is amenable.

In this paper we study the rate of the approximation by Nörlund means of Walsh–Kaczmarz–Fourier series of a function in L p (1 ≤ p ≤ ∞). As a special case, we obtain the result due to Skvortsov [Anal. Math. 7: 141–150, 1981]. Earlier results on the Walsh–Nörlund means were given by Móricz and Siddiqi [J. Approx. Theory 70: 375–389, 1992].

A priori estimates of solutions of two-point boundary value problems for two-dimensional systems of differential inequalities with singular coefficients are established.

For a certain class of orthonormal systems (ONS) on [0, 1] there exists a family of functions from L 2 (0, 1), independent from that class, such that the Fourier series with respect to each ONS of the class converges a.e. for any member of the family. Similar result holds for the summability of Fourier integrals.

It is proved that – different from the case of binary differentiation bases – in the case of strong differentiation bases a symmetrical and a complete differentiation basis are equivalent throughout the space of locally integrable functions.