Nonexpansive Mappings on New Premodular Special Space of Sequences

For different premodular, which is a generalization of modular, defined by weighted Orlicz sequence space and its prequasi operator ideal, we have examined the existence of a fixed point for both Kannan contraction and nonexpansive mappings acting on these spaces. Some numerous numerical experiments and practical applications are presented to support our results.

Local monotonicity coefficients in Orlicz sequence spaces equipped with the p-Amemiya norm

In this paper, the monotonicity is investigated with respect to Orlicz sequence space $l_{\varPhi , p}$ l Φ , p equipped with the p-Amemiya norm, and the necessary and sufficient condition is obtained to guarantee the uniform monotonicity, locally uniform monotonicity, and strict monotonicity for $l_{\varPhi , p}$ l Φ , p . This completes the results of the paper (Cui et al. in J. Math. Anal. Appl. 432:1095–1105, 2015) which were obtained for the non-atomic measure space. Local upper and lower coefficients of monotonicity at any point of the unit sphere are calculated, $l_{\varPhi , p}$ l Φ , p is calculated.

Completeness of Sequence Spaces Generated by an Orlicz Function

In this paper, we discuss about completeness property of Orlicz sequence spaces defined by an Orlicz function. Orlicz sequence space is generalization of p-summable sequence space, for every which is also an Orlicz sequence space. Based on the property of convergence sequence on norm space, we define $\Phi$-convergence sequence on Orlicz sequence space. Moreover, we define $\Phi$-Cauchy sequence and $\Phi$-complete on Orlicz sequence space. In this paper, we show the relationship between the (ordinary) convergent sequence, $\Phi$-convergent and $\Phi$-Cauchy sequences. Finally, it will also be shown that Orlicz sequence space is Banach space and $\Phi$-complete space.

Some vector valued sequence spaces of Musielak-Orlicz functions and their operator ideals

In the present paper we introduce generalized vector-valued Musielak-Orlicz sequence spacel(A,𝓜,u,p,Δr,∥·,… ,·∥)(X) and study some geometric properties like uniformly monotone, uniform Opial property for this space. Further, we discuss the operators ofs-type and operator ideals by using the sequence ofs-number (in the sense of Pietsch) under certain conditions on matrixA.

Packing Constant in Orlicz Sequence Spaces Equipped with the p-Amemiya Norm

The problem of packing spheres in Orlicz sequence spacelΦ,pequipped with the p-Amemiya norm is studied, and a geometric characteristic about the reflexivity oflΦ,pis obtained, which contains the relevant work aboutlp (p>1)and classical Orlicz spaceslΦdiscussed by Rankin, Burlak, and Cleaver. Moreover the packing constant as well as Kottman constant in this kind of spaces is calculated.

On some new modular sequence spaces

Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space ℓM which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. An important subspace of ℓ (M), which is an AK-space, is the space h (M) . We define the sequence spaces ℓM (m) and ℓ N(m), where M = (Mk) and N = (Nk) are sequences of Orlicz functions such that Mk and Nk be mutually complementary for each k. We also examine some topological properties of these spaces. We give the α−, β− and γ− duals of the sequence space h (M) and α− duals of the squence spaces ℓ (M, λ) and ℓ (N, λ).

On the Dichotomy of the Evolution Families: A Discrete-Argument Approach

We establish a discrete-time criteria guaranteeing the existence of an exponential dichotomy in the continuous-time behavior of an abstract evolution family. We prove that an evolution family acting on a Banach space X is uniformly exponentially dichotomic (with respect to its continuous-time behavior) if and only if the corresponding difference equation with the inhomogeneous term from a vector-valued Orlicz sequence space lΦ(ℕ, X) admits a solution in the same lΦ(ℕ, X). The technique of proof effectively eliminates the continuity hypothesis on the evolution family (i.e., we do not assume that U( · , s)x or U(t, · )x is continuous on [s, ∞), and respectively [0, t]). Thus, some known results given by Coffman and Schaffer, Perron, and Ta Li are extended.