we de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.

Information from the external world goes through various transformations. The learning of the original neighbourhood relations of the world using only the transformed information is examined in detail. An approximate representation consists of a nite number of discretizing points and connections between neighbouring points. The goal here is to develop such an approximate representation in a sel...

Abstract: In this paper, we study the approximate controllability for some impulsive fractional evolution hemivariational inequalities. We show the concept of mild solutions for these problems. The approximate controllability results are formulated and proved by utilizing fractional calculus, fixed points theorem of multivalued maps and properties of generalized Clarke subgradient under some ce...

Tikhonov regularization is a popular and effective method for the approximate solution of illposed problems, including Fredholm equations of the first kind. The Tikhonov method works well when the solution of the equation is well-behaved, but fails for solutions with irregularities, such as jump discontinuities. In this paper we develop a method that overcomes the limitations of the standard Ti...

A compensated compactness framework is established for sonic-subsonic approximate solutions to the two-dimensional Euler equations for steady irrotational flows that may contain stagnation points. Only crude estimates are required for establishing compactness. It follows that the set of subsonic irrotational solutions to the Euler equations is compact; thus flows with sonic points over an obsta...

We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant d, a set of n points in R indexed by time such that we can perform insertions or deletions at any point in the timeline in O(log n) amortized time. We support, for any small constant > 0, (1 + )-approximate range rep...

We consider approximate value iteration with a parameterized approximator in which the state space is partitioned and the optimal cost-to-go function over each partition is approximated by a constant. We establish performance loss bounds for policies derived from approximations associated with fixed points. These bounds identify benefits to having projection weights equal to the invariant distr...

This paper deals with approximate solutions of general (that is, without any convexity assumption) multi-objective optimization problems (MOPs). In this text, by reviewing some standard scalarization techniques we are interested in finding the relationships between ε-(weakly, properly) efficient points of an MOP and ε-optimal solutions of the related scalarized problem. For this purpose, the re...

Coupled with the concept of particular solutions and radial basis functions, a simple and effective numerical method for solving a large class of partial differential equations can be achieved. One of the difficulties of globally applying MAPS is that these methods result in a large dense matrices which in turn severely restricts the number of interpolation points, thereby affecting our ability...

We suggest a simple modification to the kd-tree search algorithm for nearest neighbor search resulting in an improved performance. The Kd-tree data structure seems to work well in finding nearest neighbors in low dimensions but its performance degrades even if the number of dimensions increases to more than three. Since the exact nearest neighbor search problem suffers from the curse of dimensi...