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

2018 ◽  
Vol 68 (1) ◽  
pp. 115-134 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Kuldip Raj
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Operator Ideals ◽  
Orlicz Sequence Space ◽  
Geometric Properties ◽  
Orlicz Functions ◽  
Opial Property ◽  
Uniform Opial Property ◽  
Vector Valued

AbstractIn 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.

scholarly journals On some new modular sequence spaces

2013 ◽  
Vol 31 (2) ◽  
pp. 55 ◽  
Author(s):  
Cigdem Asma Bektas ◽  
Gülcan Atıci
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Orlicz Sequence Space ◽  
Orlicz Functions ◽  
Orlicz 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).

scholarly journals Some Geometric Properties of Lacunary Sequence Spaces Related to Fixed Point Property

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Chirasak Mongkolkeha ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Lacunary Sequence ◽  
Fixed Point Property ◽  
Sequence Spaces ◽  
Point Property ◽  
Geometric Properties ◽  
Opial Property ◽  
Uniform Opial Property

The main purpose of this paper is considering the lacunary sequence spaces defined by Karakaya (2007), by proving the property (β) and Uniform Opial property.

scholarly journals The Opial condition in variable exponent sequence spaces with applications

2019 ◽  
Vol 35 (3) ◽  
pp. 273-279
Author(s):  
MOSTAFA BACHAR ◽  
◽  
MOHAMED A. KHAMSI ◽  
MESSAOUD BOUNKHEL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Sequence Space ◽  
Variable Exponent ◽  
Sequence Spaces ◽  
Opial Condition ◽  
Opial Property

In this work, we show an analogue to the Opial property for the coordinate-wise convergence in the variable exponent sequence space. This property allows us to prove a fixed point theorem for the mappings which are nonexpansive in the modular sense.

scholarly journals On some double almost lacunary sequence spaces defined by Orlicz functions

Filomat ◽  
2005 ◽  
pp. 35-44 ◽  
Author(s):  
Ekrem Savas ◽  
Richard Patterson
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Orlicz Function ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Orlicz Functions ◽  
Lacunary Statistical Convergence

In this paper we introduce a new concept for almost lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space. We also introduce and study almost lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

scholarly journals Linear functionals on Orlicz sequence spaces without local convexity

1992 ◽  
Vol 15 (2) ◽  
pp. 241-254 ◽  
Author(s):  
Marian Nowak
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Local Convexity ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Orlicz Sequence Space ◽  
Orlicz Sequence Spaces ◽  
Locally Convex

The general form of continuous linear functionals on an Orlicz sequence space1ϕ(non-separable and non-locally convex in general) is obtained. It is proved that the spacehϕis anM-ideal in1ϕ.

scholarly journals On matrix transformations concerning the Nakano vector-valued sequence space

2001 ◽  
Vol 26 (11) ◽  
pp. 671-678
Author(s):  
Suthep Suantai
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Real Numbers ◽  
Positive Real ◽  
The Matrix ◽  
Vector Valued ◽  
Bounded Sequences

We give the matrix characterizations from Nakano vector-valued sequence spaceℓ(X,p)andFr(X,p)into the sequence spacesEr,ℓ∞,ℓ¯∞(q),bs, andcs, wherep=(pk)andq=(qk)are bounded sequences of positive real numbers such thatPk>1for allk∈ℕandr≥0.

Generalized Orlicz-Lorentz sequence spaces and corresponding operator ideals

2014 ◽  
Vol 64 (6) ◽  
Author(s):  
Manjul Gupta ◽  
Antara Bhar
Keyword(s):  
Banach Space ◽  
Structural Properties ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Operator Ideals ◽  
Orlicz Sequence Spaces ◽  
Vector Valued

AbstractIn this paper we introduce generalized or vector-valued Orlicz-Lorentz sequence spaces l p,q,M(X) on Banach space X with the help of an Orlicz function M and for different positive indices p and q. We study their structural properties and investigate cross and topological duals of these spaces. Moreover these spaces are generalizations of vector-valued Orlicz sequence spaces l M(X) for p = q and also Lorentz sequence spaces for M(x) = x q for q ≥ 1. Lastly we prove that the operator ideals defined with the help of scalar valued sequence spaces l p,q,M and additive s-numbers are quasi-Banach operator ideals for p < q and Banach operator ideals for p ≥ q. The results of this paper are more general than the work of earlier mathematicians, say A. Pietsch, M. Kato, L. R. Acharya, etc.

scholarly journals Vector valued multiple sequence spaces defined by Orlicz function

2014 ◽  
Vol 33 (1) ◽  
pp. 67 ◽  
Author(s):  
Binod Chandra Tripathy ◽  
Rupanjali Goswami
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Multiple Sequence ◽  
Vector Valued ◽  
Inclusion Results

In this article we define some vector valued multiple sequence space defined by Orlicz function. We study some of their properties like solidness, symmetry, completeness etc and prove some inclusion results.

Sign in / Sign up

Export Citation Format

Share Document