On double sequence spaces defined by an Orlicz function on a seminormed space

In this paper we introduce and study the double sequence space m''(M,?,q) by using the Orlicz function M. Also we obtain some inclusion results involving the space m''(M,?,q).

Generalized difference sequence space defined by |$$ \bar N $$, p k| summability and an Orlicz function in seminormed space

The object of this paper is to introduce a new difference sequence space which arise from the notions of |$$ \bar N $$, p k| summability and an Orlicz function in seminormed complex linear space. Various algebraic and topological properties and certain inclusion relations involving this space have been discussed. This study generalizes results: [ALTIN, Y.—ET, M.—TRIPATHY, B. C.: The sequence space |$$ \bar N_p $$|(M, r, q, s) on seminormed spaces, Appl. Math. Comput. 154 (2004), 423–430], [BHARDWAJ, V. K.—SINGH, N.: Some sequence spaces defined by |$$ \bar N $$, p n| summability, Demonstratio Math. 32 (1999), 539–546] and [BHARDWAJ, V. K.—SINGH, N.: Some sequence spaces defined by |$$ \bar N $$, p n| summability and an Orlicz function, Indian J. Pure Appl. Math. 31 (2000), 319–325].

On lacunary generalized difference sequence spaces defined by Orlicz functions in a seminormed space and Δqm $\Delta _q^m $ -lacunary statistical convergence

The main purpose of this paper is to introduce a new concept of

Strong invariant A-summability with respect to a sequence of modulus functions in a seminormed space

The object of this paper is to introduce some new strongly invariant

Generalized difference sequence spaces on seminormed space defined by Orlicz functions

In this paper we define the sequence space ℓM (Δm, p, q, s) on a seminormed complex linear space by using an Orlicz function. We study its different algebraic and topological properties like solidness, symmetricity, monotonicity, convergence free etc. We prove some inclusion relations involving ℓM (Δm, p, q, s).