Generalized vector valued double sequence space using modulus function

Abstract

In this paper, we introduce a generalized vector valued paranormed double sequence space $ F^{2}(E,p,f,s) $, using modulus function $ f $, where $ p=(p_{nk}) $ is a sequence of non-negative real numbers, $ s\geq 0 $ and the elements are chosen from a seminormed space $ (E, q_{E}) $. Results regarding completeness, normality, $ K_{2} $-space, co-ordinatewise convergence etc. are derived. Further, a study of multiplier sets, ideals, notion of statistical convergence and ($ p_{nk} $ )-Ces\'aro summability in the space $ F^{2}(E,p,f,s) $ is also made.

Extension of lacunary statistical convergence on vector valued double difference sequence space

“…In this case, we write x k −→ (S θ ). Recently Bilgin [24], Jinlu Li [20], Karakaya et al [12], Ç akalli [8], Basu et al ([1], [2]), Savas et al [7] and many others have extended the concept of lacunary statistical convergence and continued this study by introducing new sequence spaces using modulus functions, Orlicz functions, infinite matrices etc.…”