In the present paper we introduce some vector-valued multiplier difference sequence spaces defined by a Musielak-Orlicz function, concepts of lacunary convergence and strong (A, u)-convergence, where A = (aik) is an infinite matrix of complex numbers and u = (ui) be any sequence of strictly positive real numbers. We also make an effort to study some topological properties and some inclusion rel...

In this paper, we study two classes of Kirchhoff-type problems set on a double-phase framework. That is, the functional space where finding solutions coincides with Musielak–Orlicz–Sobolev $$W^{1,{\mathcal {H}}}_0(\Omega )$$ , modular function $${\mathcal {H}}$$ related to so-called operator. Via variational approach, provide existence and multiplicity results.

in this paper we introduce entire sequence spaces defined by a sequence of modulus functions . we study some topological properties of these spaces and prove some inclusion relations.

The aim of this paper is to characterize one-complemented subspaces of finite codimension in the Musielak–Orlicz sequence space l . We generalize the well-known fact (Ann. Mat. Pura Appl. 152 (1988) 53; Period. Math. Hungar. 22 (1991) 161; Classical Banach Spaces I, Springer, Berlin, 1977) that a subspace of finite codimension in lp, 1 p<∞, is one-complemented if and only if it can be expressed...

Let φ : ℝ(n) × [0, ∞)→[0, ∞) be a Musielak-Orlicz function and A an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, H(A)(φ)(ℝ(n)), via the grand maximal function. The authors then obtain some real-variable characterizations of H(A)(φ)(ℝ(n)) in terms of the radial, the nontangential, and the tangential maximal functions, which general...

and Applied Analysis 3 Put LM X { u ∈ XT : ρM λu < ∞ for some λ > 0 } . 1.5 Then the Musielak-Orlicz-Bochner function space ‖u‖ inf k>0 1 k [ 1 ρM ku ] 1.6 is Banach space. If X R, LM R is said to be Musielak-Orlicz function space. Set K u { k > 0 : 1 k ( 1 ρM ku ) ‖u‖ } . 1.7 In particular, the set K u can be nonempty. To show that, we give a proposition. Proposition 1.1. If limu→∞ M t, u /u ∞...