A generalisation of the Ostrowski integral inequality for mappings of bounded variation and applications for general quadrature formulae are given.

A classical theorem by Lancret says that a curve in Euclidean 3-space is of constant slope if and only if its ratio of curvature and torsion is constant. In this paper we study Lancret type problems for curves in Sasakian 3-manifolds.

It has recently been shown that a Banach space enjoys the weak fixed point property if it is ε0-inquadrate for some ε0 < 2 and has WORTH; that is, if then, ║xn — x║ — ║xn + x║ → 0, for all x. We establish the stronger conclusion of weak normal structure under the substantially weaker assumption that the space has WORTH and is ‘ε0-inquadrate in every direction’ for some ε0 < 2.

Explicit expressions for the Green's functions due to a point force in one of two half space fluids are presented for the case when inertial effects of the fluid are negligible (Stokes flow) and the interface between the two fluids is considered to be flat due to the action of surface tension. The analytic expressions are discussed in terms of singularity diagrams. For the case of a force parallel to the interface a first approximation to the interface displacement is made.

Let ${\mathcal{S}}$ denote the class of analytic and univalent functions in $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ which are of the form $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$. We determine sharp estimates for the Toeplitz determinants whose elements are the Taylor coefficients of functions in ${\mathcal{S}}$ and certain of its subclasses. We also discuss similar problems for typically real functions.

In the last three years a number of people have investigated the orthogonality relations for square integrable representations of non-unimodular groups, extending the known results for the unimodular case. The results are stated in the language of left (or generalized) Hilbert algebras. This paper is devoted to proving the orthogonality relations without recourse to left Hilbert algebra techniques. Our main technical tool is to realise the square integrable representation in question in a reproducing kernel Hilbert space.

We follow the idea of generalising the notion of classical iterated function systems, as presented by Mihail and Miculescu. We give their deliberations a more general setting and, using this general approach, study the generic aspect of the problem of existence of an attractor of a function system.

We present a natural topology compatible with the Mosco convergence of sequences of closed convex sets in a reflexive space, and characterise the topology in terms of the continuity of the distance between convex sets and fixed weakly compact ones. When the space is separable, the topology is Polish. As an application, we show that in this context, most closed convex sets are almost Chebyshev, a result that fails for the stronger Hausdorff metric topology.

The main purpose of this paper is to generalise a supersolvability theorem of O. U. Kramer to a saturated formation containing the class of supersolvable groups. As applications, we generalise some results recently obtained by some scholars.

The concept of efficiency (Pareto optimum) is used to formulate duality for multiobjective fractional programming problems. We consider programs where the components of the objective function have non-negative and convex numerators while the denominators are concave and positive. For this case the Mond-Weir extension of Bector dual analogy is given. We also give the Schaible type vector dual. The case where functions are ρ-convex (weakly or strongly convex) is also considered.

This note presents an analogue of the classical Heisenberg-Weyl uncertainty principle for the Dunkl transform on ℝN. Its proof is based on expansions with respect to generalised Hermite functions.

For the purpose of this paper a logic is defined to be a non-empty set of propositions which is partially ordered by a relation of logical implication, denoted by “≤”, and which, as a poset, is orthocomplemented by a unary operation of negation. The negation of the proposition x is denoted by NX and the least element in the logic is denoted by 0, we write NO = 1.

A binary operation “→” is introduced into a logic, the operation is interpreted as material implication so that “x → y” is a proposition of the logic and is read as “x materially implies y”. If material implication has the properties

11. (x → 0) = NX, 12. if x ≤ y then (z → x) ≤ (z → y), 13. if x ≤ y then x ≤ (y ≤ z)= x → z, 14. x ≤ {y → N(y → Nx)}, then the logic is an orthomodular lattice. The lattice operations of join and meet are given by x ∨ y = Nx → N(Nx → Ny) x ∧ y = N(X → N(x → y)) and, in terms of the lattice operations, the material implication is given by (x → y) = (y ∧ x) ∨ NX.

Moreover the logic is a Boolean algebra if, and only if, in addition to the properties above, material implication satifies 15. (x → y) = (Ny → Nx).

We prove a Korovkin-type theorem on approximation of bivariate functions in the space of B-continuous functions (introduced by K. Bögel in 1934). As consequences, some sequences of uniformly approximating pseudopolynomials are obtained.

The existence of globally attractive order intervals for some strongly monotone discrete dynamical systems in ordered Banach spaces is first proved under some appropriate conditions. With the strict sublinearity assumption, threshold results on global asymptotic stability are then obtained. As applications, the global asymptotic behaviours of nonnegative solutions for time-periodic parabolic equations and cooperative systems of ordinary differential equations are discussed and some biological interpretations and concrete application examples are also given.

We begin the study of Hankel matrices whose entries are logarithmic coefficients of univalent functions and give sharp bounds for the second Hankel determinant of logarithmic coefficients of convex and starlike functions.

Let X be a tree and f be a continuous map from X into itself. Denote by P(f) and R(f) the set of periodic points and the set of recurrent points of f respectively. We show in this note that the centre is and the depth of the centre is at most 3. Furthermore we have .

A new measure of weak noncompactness is introduced. A logarithmic convexity-type result on the behaviour of this measure applied to bounded linear operators under real interpolation is proved. In particular, it gives a new proof of the theorem showing that if at least one of the operators T: Ai → Bi, i = 0, 1 is weakly compact, then so is T : Aθ,p → Bθ,p for all 0 < θ < 1 and 1 < P < ∞.

In this paper we give an elementary method for classifying conjugacy classes of involutions in a Coxeter group (W, S). The classification is in terms of (W-equivalence classes of certain subsets of S).

Let S = {x1, x2, …, xn} be a set of distinct positive integers. The n × n matrix [S] = (Sij), where Sij, = (xi, xj), the greatest common divisor of xi, and xj, is called the greatest common divisor (GCD) matrix on S. H.J.S. Smith showed that the determinant of the matrix [E(n)], E(n) = { 1,2, …, n}, is ø(1)ø(2) … ø(n), where ø(x) is Euler's totient function. We extend Smith's result by considering sets S = {x1, x2, … xn} with the property that for all i and j, (xi, xj) is in S.

“Fuzzy theories” and “distributive laws” are used to define “fuzzy systems” in an arbitrary category. The resulting minimal realization theory provides new insights even in classical cases (so that, for non-deterministic sequential machines, the minimal realization problem is reformulated in terms of the structure of join-irreducibles in finite lattices). The definition of “fuzzy theory” is of independent interest and meshes well with philosophical aspects of fuzzy set theory.