Sliding window rough measurable function on Riesz Triple Almost \((\lambda_{m_{i}}\mu_{n_{\ell}}\gamma_{k_{j}})\) Lacunary \(\chi^{3}_{R_{\lambda_{m_{i}}\mu_{n_{\ell}}\gamma_{k_{j}}}}\) sequence spaces defined by a Orlicz function

Authors

Ayhan Esi - Department of Mathematics,Adiyaman University,02040,Adiyaman, Turkey
Nagarajan Subramanian - Department of Mathematics,SASTRA University,Thanjavur-613 401, India

Abstract

In this paper we introduce a new concept for generalized sliding window rough measurable function on almost $\left(\lambda_{m_{i}}\mu_{n_{\ell}}\gamma_{k_{j}}\right)$ convergence in $\chi^{3}_{R_{\lambda_{m_{i}}\mu_{n_{\ell}}\gamma_{k_{j}}}}$-Riesz spaces strong $P$-convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We also introduce and study sliding window rough statistical convergence of generalized sliding window rough measurable function on almost $\left(\lambda_{m_{i}}\mu_{n_{\ell}}\gamma_{k_{j}}\right)$ convergence in $\chi^{3}_{R_{\lambda_{m_{i}}\mu_{n_{\ell}}\gamma_{k_{j}}}}$-Riesz space and also some inclusion theorems are discussed.

Keywords

Analytic sequence, Orlicz function, double sequences, $\chi$-sequence, Riesz space, Riesz convergence, Pringsheim convergence

References