We prove a joint universality theorem in the Voronin sense for the periodic Hurwitz zeta-functions.

Let R be a commutative ring. It is shown that if an R-module M is a sum of δ-local submodules and a semisimple projective submodule, then every finitely generated submodule of M is δ-supplemented. From this result, we conclude that finitely generated δ-supplemented modules over commutative rings are amply δ-supplemented.

Let Ω be a bounded convex domain in R2 with a smooth boundary. Let 0 < γ < 1. Let be a solution, positive in Ω, of

Then the function uα is concave for α = (l–γ)/2.

The paper is concerned with an extension of the inequality 1 - u(2nt) ≤ 4n[1-u(t)] for u(t) the real part of a characteristic function. The main result is that the inequality in fact holds for all positive integer n and not only powers of 2. Certain consequences are deduced and a brief discussion is given of the circumstances under which equality holds.

The ranges of the Y-integral transform in some spaces of functions are described.

A Banach space has the Radon–Nikodym Property if and only if every continuous weak* lower semi–continuous gauge on the dual space has a point of its domain where its subdifferential is contained in the natural embedding.

This paper Presents a multivalued version of an approximation result of Ky Fan (Math. Z.112 (1969)) for maps.

We study the groups of isometries for Hilbert metrics on bounded open convex domains in ℝn and show that if  is such a set with a strictly convex boundary, the Hilbert geometry is asymptotically Riemannian at infinity. As a consequence of this result, we prove there are no Hausdorff quotients of  by isometry subgroups with finite volume except when ∂ is an ellipsoid.

Variational inequality theory provides techniques for solving a variety of applied problems in science and engineering. Recently Noor considered some interesting general nonlinear and linear variational inequalities in a series of papers and proved the existence and uniqueness of solutions by a fixed point technique developed by Glowinski, Lions and Tremolieres and also by a fixed point technique of Lions and Stampacchia. But there are several inaccuracies in his proofs and here they have been removed and correct formulation of the theorems are stated and proved and relationships are clearly shown. The existence of solution necessitates an additional condition in one case, and less condition in the other, but uniqueness can be proved without the condition that the operator be antimonotone.

After defining a generalized C-fraction (a kind of Jacobi-Perron algorithm) for an n-tuple of formal power series over (n ≥ 2), the connection between interruptions in the algorithm and linear dependence over [x] of the power series is studied.

Examples will be given showing that the algorithm behaves in a way similar to the Jacobi-Perron algorithm for an n-tuple of real numbers (the gcd-algorithm): there do exist n-tuples of formal power series f(1), f(2), …, f(n) with a C-n-fraction without interruptions but for which 1, f(1), f(2), …, f(n) is nevertheless linearly dependent over [x].

Moreover an example will be given of algebraic functions f, g of degree n over [x] (formally defined) for which the C-n-fraction for f, f2, …, fn has just one interruption and that for g, g2, …, gn 1 none, while of course 1. f, f2, …, fn and 1, g, g2, …, gn admit (only) one dependence relation over [x].

It has recently been shown that discontinuous functional calculi exist for certain commutative Banach algebras. Such an algebra thus possesses two distinct calculi so that there exist analytic functions whose action on the algebra is not uniquely determined. In this note a method is given for constructing commutative Banach algebras which admit two inequivalent complete norm topologies and the result is applied to show that the action of any non-algebraic analytic function may fail to be uniquely defined.

Let p be an odd prime and let G be a finite p-group such that xZ(G)⊆xG, for all x∈G∖Z(G), where xG denotes the conjugacy class of x in G. Then G has a noninner automorphism of order p leaving the Frattini subgroup Φ(G) elementwise fixed.

In this paper we prove the following existence and uniqueness theorem for the nonlinear complementarity problem by using the Banach contraction principle. If T: K → H is strongly monotone and lipschitzian with k2 < 2c < k2+1, then there is a unique y ∈ K, such that Ty ∈ K* and (Ty, y) = 0 where H is a Hilbert space, K is a closed convex cone in H, and K* the polar cone.

We prove the existence of an optimal control in Banach spaces for a system characterized by Hammerstein operator equations.

This paper is concerned with the almost sure convergence for arrays of independent, but not necessarily identically distributed, random variables. We show that Kolmogorov's law of the iterated logarithm does not hold for arrays and obtain an analogue of Kolmogorov's law.

We introduce the notion of generalised 3-Sasakian structure on a manifold and show that a totally umbilical, but not totally geodesic, proper QR-submanifold of a quaternion Kaehlerian manifold is an extrinsic sphere and inherits such a structure.

There are several geometric characterizations of inner product spaces amongst the normed linear spaces. Mahlon M. Day's refinement “rhombi suffice as well as parallelograms”, of P. Jordan and J. von Neumann parallelogram law is well known. There are some characterizations which employ various notions of orthogonality. For example, it is known that if in a normed linear space Birkhoff-James orthogonality implies isosceles orthogonality. For example, it is known that if in a normed linear space Birkhoff-James orthogonality implies isosceles orthogonality then the space is an inner product space; geometrically it means that if the diagonals of a rectangle, with sides perpendicular in Birkhoff-James sense, are equal then the space is an inner product space. In the main result of this note we improve upon this characterization and show that here unit squares suffice as well as rectangles.

We deal with the dual Banach algebras for a locally compact group G. We investigate compact left multipliers on , and prove that the existence of a compact left multiplier on is equivalent to compactness of G. We also describe some classes of left completely continuous elements in .

In the present paper, a coupled algorithm refining recursively the Hermite–Hadamard inequality on a simplex is investigated. Our approach allows us to express the integral mean value $M_{f}$ of a convex function $f$ on a simplex as both the limit of sequences and sum of series involving iterative lower and upper bounds of $M_{f}$. Two examples of interest are discussed.

We find a new refinement of Fine’s partition theorem on partitions into distinct parts with the minimum part odd. As a consequence, we obtain two companion partition identities. Both analytic and combinatorial proofs are provided.