The set of interval Hausdorff continuous functions constitutes the largest space preserving basic algebraic and topological structural properties of continuous functions, such as linearity, ring structure, Dedekind order completeness, etc. Spaces of interval functions have important applications not only in the construction of numerical methods and algorithms, but to problems in abstract areas ...

The lattice of z-ideals of the ring C(X) of real-valued continuous functions on a completely regular Hausdorff space X has been shown by Mart́ınez and Zenk to be a complete Heyting algebra with certain properties. We show that these properties are due only to the fact that C(X) is an f -ring with bounded inversion. This we do by studying lattices of algebraic z-ideals of abstract f -rings with b...

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...

It is well known that a commutative ring R is complemented (that is, given a ∈ R there exists b ∈ R such that ab = 0 and a + b is a regular element) if an only if the total ring of quotients of R is von Neumann regular. We consider generalizations of the notion of a complemented ring and their implications for the total ring of quotients. We then look at the specific case when the ring is a rin...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

We develop a notion of derivative of a real-valued function on a Banach space, called the L-derivative, which is constructed by introducing a generalization of Lipschitz constant of a map. As with the Clarke gradient, the values of the L-derivative of a function are non-empty weak* compact and convex subsets of the dual of the Banach space. The L-derivative, however, is shown to be upper semi c...

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...