The aim of this paper is to set up appropriate uniform convergence spaces in which to reformulate and enrich the Order Completion Method [25] for nonlinear PDEs. In this regard, we consider an appropriate space ML (X) of normal lower semi-continuous functions. The space ML (X) appears in the ring theory of C (X) and its various extensions [15], as well as in the theory of nonlinear, PDEs [25] a...

Theory and applications have shown that there are two important types of convergence for convex functions: pointwise convergence and convergence in a topology induced by the convergence of their epigraphs. We show that these two types of convergence are equivalent on the class of convex functions which are equi-lower semicontinuous. This turns out to be maximal classes of convex functions for w...

The inherent iteration required in the multidisciplinary design problem allows the design problem to cast as a dynamical system. The iteration in design is a resultant of the two rootfinding problems. The first root-finding problem is in seeking out candidate designs while the second is in optimizing the candidate designs. Viewing the root-finding schema as a dynamical system allows the applica...

This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of functions in an extended multifunction space (Sengupta and Ray, 2000), and the topological theory of convergence. Order, chaos, and complexity are described as dis...

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

In 2000, Kostyrko, Salat, and Wilczynski introduced and studied the concept of I-convergence of sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of Number Theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article we introduce the double sequence spaces     2 0 2...