Some generalized difference sequence spaces of invariant means defined by Orlicz functions (Q2575975)

Summary: We define the sequence spaces \([w^{\theta}, M, p, u, \Delta]_{\sigma}\), \([w^{\theta}, M, p, u, \Delta]_{\sigma}^0\) and \([w^{\theta }, M, p, u, \Delta]_{\sigma}^{\infty}\) by combining the concepts of Orlicz functions, invariant means, and lacunary convergence. We also study some inclusion relations and linearity properties of the above-mentioned spaces. These are generalizations of those defined and studied by \textit{E.~Savaş} and \textit{B.~E.\ Rhoades} [Math.\ Inequal.\ Appl.\ 5, No.~2, 271--281 (2002; Zbl 1010.46006)] and in other preceding works.