‎‎‎Given a fuzzy normed space, we will introduce the notion of fuzzy near best Approximation as a generalization of the notion of fuzzy best Approximation. Some basic properties are characterized and also many examples for illustration are presented. Also, the hereditary properties of the fuzzy near best Approximation on direct sum and tensor product of linear spaces are discussed.

Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of their unifying role and their successes in applications. Filter banks, which lie at the heart of wavelet-based algorithms, have become standard signal processing operators, used routinely in applications ranging from compression to modems. The contributions of wavelets have often been in the subtle interplay between discrete-time and continuous-time signal processing. The purpose of this article is to look at recent wavelet advances from a signal processing perspective. In particular, Approximation results are reviewed, and the implication on compression algorithms is discussed. New constructions and open problems are also addressed. Finding a good basis to solve aproblem dates at least back to Fourier and his investigation of the heat equation. The series proposed by Fourier has several distinguishing features: The series is able to represent any finite energy function on an interval. The basis functions are eigenfunctions of linear shift invariant systems or, in other words, Fourier series diagonalize linear, shift invariant operators.

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In this paper, we study wavelet Approximation of the Chebyshev polyno-mials of the first, second, third, and fourth kinds. We estimate the wavelet Approximation of a function f having bounded first derivatives.

In this manuscript we suggest a fast adaptive distributed method for maximum likelihood Approximation (MLA) in multiple view object localization problem. For this purpose, we use "up to scale" property of projective geometry and by defining coefficients for convergence criterion, we increase the convergence speed of the consensus algorithm. We try to present a mathematical model for the problem. We use two types of error function. The proposed method uses maximum likelihood for obtaining its best parameters. Our approach utilizes "up to scale" property in projective geometry to reach the consensus quickly. The difference between nodes' values and meanwhile consensus values are evaluated by two error functions. To estimate consensus value in the second error function, we used local weighted average of each node. At the last of the paper, we prove our claims by experimental results.