Neoclassical Analysis: Calculus Closer to the Real World
Nova Science Publishers, 2007 - Mathematics - 396 pages
Neoclassical analysis extends methods of classical calculus to reflect uncertainties that arise in computations and measurements. In it, ordinary structures of analysis, that is, functions, sequences, series, and operators, are studied by means of fuzzy concepts: fuzzy limits, fuzzy continuity, and fuzzy derivatives. For example, continuous functions, which are studied in the classical analysis, become a part of the set of the fuzzy continuous functions studied in neoclassical analysis. Aiming at representation of uncertainties and imprecision and extending the scope of the classical calculus and analysis, neoclassical analysis makes, at the same time, methods of the classical calculus more precise with respect to real life applications. Consequently, new results are obtained extending and even completing classical theorems. In addition, facilities of analytical methods for various applications also become more broad and efficient.
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Fuzzy Continuous Functions
9 other sections not shown
2-fuzzy approximate arbitrary B-conditional binary relation Burgin called Cauchy Criterion classical calculus classical result closed interval computation concept Consequently convergent sequence defined Definition denoted diverges equal example extended weak finite following result function fix fuzzy continuous functions fuzzy convergence fuzzy differentiable fuzzy limits fuzzy set theory global implies the following implies the inequality inequality fix interval analysis left right Leibniz Lemma Let us assume Let us consider Let us take lim h mapping mathematical mathematicians membership function metric spaces monotone natural numbers neoclassical analysis partial function partial limit point a e possible problems Proof properties r-continuous r-converges r-derivative of fix r-fundamental r-lim r-limit real functions real numbers Remark Riemann integral Section sequence h sequence of functions statistical convergence strong centered subsequence subset summability Theorem is proved topological spaces two-sided uniformly converges values weak centered weak derivative weak fuzzy derivatives