Volume 13, Issue 1

We exhibit a class of nonlinear operators with the property that their iterates converge to their unique fixed points even when computational errors are present. We also show that most (in the sense of the Baire category) elements in an appropriate complete metric space of operators do, in fact, possess this property.

A necessary and sufficient condition is established for a complex-valued function to be jointly ℂ-differentiable at a given point by applying Hartogs' main theorem.

We investigate the functional equation for f : M → S , where M is an Abelian 2- and 3-divisible group and S is an abstract convex cone. The motivation for studying this equation came from results due to Tiberiu Trief [J. Math. Anal. Appl. 250: 579–588, 2000] and Young Whan Lee [Math. Anal. Appl. 270: 590–601, 2002], where equation (1) was considered with constants a = 3, b = 2 and a = 9 and b = 4, respectively.

We introduce the notion of a random partition of the stochastic interval [ τ 0 , τ ∞ ] as an analogy to the classical case and characterize the predictable processes associated with such partitions. Also we identify the operator algebras connected with the stochastic integrals of predictable processes and examine their mutual relations.

Let K be a convex cone in a real Banach space. The main purpose of this paper is to show that for a regular cosine family { F t : t ∈ ℝ} of linear continuous multifunctions F t : K → cc ( X ) there exists a linear continuous multifunction H : K → cc ( K ) such that

In this paper, we give a fixed point theorem for triangular mappings whose derivatives are bounded.

The notion of the resolvability of a topological space was introduced by E. Hewitt [Duke Math. J. 10: 309–333, 1943]. Recently it was understood that this notion is also important in the study of w -primitives, especially in the case of nonmetrizable spaces. In the present paper a criterion for the resolvability of a topological space at a point (“local resolvability”) is given. This criterion, stated in terms of oscillation and quasicontinuity, permits to conclude, for instance, that on irresolvable spaces no positive continuous real-valued function has an w -primitive. The result is strenghtened in the case of SI-spaces. It is also shown that every nonnegative upper semicontinuous function on a resolvable Baire space has an w -primitive.

Hörmander spaces , where k is a weight and Ω is an open subset of , and their topological duals are well-known distributions spaces playing an essential role in the study of linear partial differential operators. In this paper, we define vector-valued Hörmander-Beurling spaces and study some of their most interesting properties.

A pair of Mond-Weir type second order mixed symmetric duals is presented for a class of non-differentiable multi-objective non-linear programming problems with multiple arguments. We establish duality theorems for the new pair of dual models under second order generalized convexity assumptions. This mixed second order dual formulation unifies the two existing second order symmetric dual formulations in the literature. Many recent works on symmetric duality are obtained as special cases of the results established in the present paper.

In this paper, we give a new nonempty intersection theorem in general topological spaces without convexity structure. As its applications, some new minimax inequalities are obtained in general topological spaces without convexity structure.