Orlicz-Quasi-Cauchy double sequence spaces for RH-regular matrix

Abstract

In this research paper we pioneer, a new double sequence space called Orlicz-Quasi-Cauchy double sequence space, (M,A,Δ) OQC . We investigate continuity type properties of Orlicz double function defined on a double subset A × A of R 2 into R and study some vital results related to uniform continuity. In the last we also make an attempt to prove some topological properties of (M,A,Δ) OQC .

On the domain of Cesàro matrix defined by weighted means in ℓ t ( . ) , and its pre-quasi ideal with some applications

“…Newly, many authors in the literature have discussed a few non-absolute type sequence spaces and presented new interesting articles, for example, see Mursaleen and Noman [27,28], and Mursaleen and Bas ¸ar [25]. Many authors have introduced and studied different sequence spaces to fill in gaps in the literature, such as Tripathy [39,40], Altin et al [3], Tripathy et al [41,42], Khan et al [21], Hazarika and Esi [15], Raj et al [36] and Yaying et al [43,44]. In view of Banach fixed point theorem [8], Kannan [19] offered an example of a class of operators with the same fixed point actions as contractions though that fails to be continuous.…”

Generalized statistically pre-Cauchy triple sequences via Orlicz functions

“…These concepts are also studied of double and triple sequences. The different notions on the statistical convergence of triple sequences due to Şahiner et al [30] and Şahiner and Tripathy [33] and others (see [6,7,[18][19][20][21][22]27]).…”