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Abstract: We enlarge the class of fuzzy transforms (F-transforms) by considering different types of fuzzy partitions. New types of F-transforms are constructed based on B-splines, Shepard kernels, Bernstein basis polynomials and Favard–Szász–Mirakjan type operators. We study approximation properties of F-transforms. Particular cases of the classical Korovkin''s theorems are presented, together with new error estimates for different types of fuzzy transforms. It turns out that F-transforms can be studied in the framework of classical approximation theory. [Copyright &y& Elsevier]

Abstract: In the framework of the pseudo-analysis the classical space is generalized and there are proved important properties of introduced space. Three types of convergence of sequences of measurable functions are considered in this space. The inequalities for integrals based on pseudo-integral have been recently proposed as the Hölder, Minkowski and Markov inequalities, which are applied in observing relationship among introduced convergences. [Copyright &y& Elsevier]