On generalized invariant statistical convergence of weight g

Abstract

The goal of this paper is to introduce the concept of λ-invariant statistical convergence of weight $g:[0,\infty )\to [0,\infty )$ where $g(x_n)\to \infty$ for any sequence $(x_n)$ in $[0,\infty )$ with $x_n\to \infty .$ We also investigate some relations between λ-invariant statistical convergence of weight g and strong $(V,(\lambda ,\sigma ))$-summability of weight g and then the relations between the spaces $[V_p^g,(\lambda ,\sigma ),f]$ and $S_{(\lambda ,\sigma )}^g.$

Keywords:

• Cesàro summability
• invariant convergence
• modulus function
• statistical convergence
• weight function g

2000 MATHEMATICS SUBJECT CLASSIFICATION::

• 40A05
• 40A35
• 46A45