Let A and B be nonempty subsets of a metric space X and also T :for some > 0. We call pair A, B an approximate best proximity pair. In this paper, definitions of approximate best proximity pair for a map and two maps, their diameters, T -minimizing a sequence are given in a metric space.
We define approximate fixed point and fuzzy diameter in fuzzy norm spaces. We prove theorems for various types of well-known generalized contractions on fuzzy norm spaces with the use of two general lemmas that are given regarding approximate fixed points of operators on fuzzy norm spaces.
In this work, we applied a new method for solving the linear weakly singular mixed Volterra-Fredholm integral equations. We now begin the theoretical study with acquirement of the variational form; in addition, we are using Bernstein spectral Galerkin method to be approximate to my problems. We estimate the error of the method by proved some theorems. Moreover, in the final section, we solved some numerical examples.
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