f(?, ?)-statistical convergence of order (?)over-tildefor double sequences

Abstract

New concepts of f(lambda mu)-statistical convergence for double sequences of order (alpha) over tilde and strong f(lambda mu)-Cesaro summability for double sequences of order (alpha) over tilde are introduced for sequences of (complex or real) numbers. Furthermore, we give the relationship between the spaces W-(alpha) over tilde ,0(2) (f, lambda, mu), W-(alpha) over tilde(2) (f, lambda, mu) and W-(alpha) over tilde,infinity(2) (f, lambda, mu). Then we express the properties of strong f(lambda,mu)-Cesaro summability of order (beta) over tilde which is related to strong f(lambda,mu)-Cesaro summability of order (alpha) over tilde. Also, some relations between f(lambda,mu)-statistical convergence of order (alpha) over tilde and strong f(lambda,mu)-Cesero summability of order (alpha) over tilde are given.