We show several examples of n.a. valued fields with involution. Then, by means of a field of this kind, we introduce “n.a. Hilbert spaces” in which the norm comes from a certain hermitian sesquilinear form. We study these spaces and the algebra of bounded operators which are defined on them and have an adjoint. Essential differences with respect to the usual case are observed.

A classical question in the theory of functional equations is the following: “When is it true that a function which approximately satisfies a functional equation E must be close to an exact solution of E?” If the problem accepts a solution, we say that the equation E is stable. The first stability problem concerning group homomorphisms was raised by Ulam [30] in 1940. We are given a group G and...

A. George and P. Veeramani, 1994. On some results in fuzzy metric space, Fuzzy Sets and Systems, vol. 64, 395-399. B. Schweizer, H. Sherwood, and R. M. Tardi®,1988. Contractions on PMspace examples and counter examples, Stochastica vol. 1, 5–17. D. Mihet, 2004. A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, vol. 144, 431–439. D. Mihet, 2008. Fuzzy -contractive mapp...

a new algorithm for classification of dmus to efficient and inefficient units in data envelopment analysis is presented. this algorithm uses the non-archimedean charnes-cooper-rhodes[1] (ccr) model. also, it applies an assurance value for the non-archimedean                          using only simple computations on inputs and outputs of dmus (see [18]). the convergence and efficiency of the ne...

The aim of this paper is to introduce the concepts of compatible mappings and compatible mappings of type (R) in non-Archimedean Menger probabilistic normed spaces and to study the existence problems of common fixed points for compatible mappings of type (R), also, we give an applications by using the main theorems.

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (Dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out several examples. One motivation is to see wheth...

In these lecture notes we present an introduction to non-standard analysis especially written for the community of mathematicians, physi­ cists and engineers who do research on J. F. Colombeau’ theory of new generalized functions and its applications. The main purpose of our non-standard approach to Colombeau’ theory is the improvement of the properties of the scalars of the varieties of spaces...

Axiomatizations of measurement systems usually require an axiom--called an Archimedean axiom-that allows quantities to be compared. This type of axiom has a different form from the other measurement axioms, and cannot-except in the most trivial cases-be empirically verified. In this paper, representation theorems for extensive measurement structures without Archimedean axioms are given. Such st...

In this paper, we explain a new generalized contractive condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresp...