Convergence without Limits

摘要

In this paper, we study problems of function approximation and numerical differentiation in the context of neoclassical analysis. As a tool for approximation, we use fuzzy contraction and fuzzy convergence of number sequences where fuzzy convergence is one of the basic concepts of neoclassical analysis and fuzzy contraction is introduced in this paper. Relations between fuzzy contraction and fuzzy convergence are explored. To model numerical differentiation, left and right displaced fuzzy derivatives are introduced and studied. Left and right displaced fuzzy derivatives further develop structures of left and right fuzzy derivatives from neoclassical analysis, as well as classical left and right derivatives.