Abstract
This paper presents three definitions which are natural combination of the definitions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, and Wijsman convergence. In addition, we also present asymptotically equivalent (Wijsman sense) analogs of theorems in Patterson and Savaş (2006).
Highlights
In 1993, Marouf presented definitions for asymptotically equivalent and asymptotic regular matrices
The concept of Wijsman statistical convergence is implementation of the concept of statistical convergence to sequences of sets presented by Nuray and Rhoades in 2012
The concept of Wijsman lacunary statistical convergence was presented by Ulusu and Nuray in 2012
Summary
Department of Mathematics, Faculty of Science and Literature, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey This paper presents three definitions which are natural combination of the definitions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, and Wijsman convergence. In addition, we also present asymptotically equivalent (Wijsman sense) analogs of theorems in Patterson and Savas (2006).
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