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A NEW STRUCTURE OF SPACES USING THE FRAMEWORK OF GENERALIZED ∆-OPERATOR METHOD
Abstract
The focus of the study in the this paper is to introduce the space L ϑ s p, ∆ w g. The corresponding completeness property will be determined. Also, various topological properties will be enlightened. Mathematics Subject Classication (2010): 46B45 46A45 46B99.
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The structure of the Ces\`{a}ro spaces were investigated by various authors as cited in the text. The scenario of this manuscript is to bring out the spaces of Ces\`{a}ro type for . We will study some of their basic topological properties and obtain some inclusion relations concerning these spaces.
In the present paper, we introduce a new difference sequence space rqB (u,p) by using the Riesz mean and the B- difference matrix. We show rqB (u,p) is a complete linear metric space and is linearly isomorphic to the space l(p). We have also computed its α-, ß- and γ-duals. Furthermore, we have constructed the basis of rqB (u,p)and characterize a matrix class rqB (u,p), l∞.
In this paper, we introduce a new sequence space involving Lacunary
sequence and investigate k − NUC property of this space which is equipped with
the Luxemburg norm.
On the Orlicz- Cesaro sequence spaces ( ces ) which are defined by using Orlicz function , we show that the space ces equipped with both Amemiya and Luxemburg norms possesses uniform Opial property and uniform Kadec-Klee property if satisfy the 52 -condition.
In this paper, we define the sequence spaces ) , c f " and 0 c be the linear spaces of bounded, convergent, and null sequences ) ( k x x with complex terms, respectively, normed by k k x x sup f
Necessary and sufficient conditions under which the Cesàro-Orlicz sequence spaceces
ϕ
is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spacesces
ϕ
have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements inces
ϕ
can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spacesces
ϕ
are given.
We introduce new sequence space involving lacunary sequence connected with Cesaro sequence space and examine some geometric properties of this space equipped with Luxemburg norm.
The difference sequence space m(Æ,p,Δ(r)), which is a generalization of the space m(Æ) introduced and studied by Sargent (1960), was defined by Çolak and Et (2005). In this paper we establish some geometric inequalities for this space.
The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing.
In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student.
One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.
In this paper define the spaces l ∞ (Δ), c(Δ), and c 0 (Δ), where for instance l ∞ (Δ) = {x=(x k ):sup k |x k -x k + l |< ∞} , and compute their duals (continuous dual, α-dual, β-dual and γ-dual). We also determine necessary and sufficient conditions for a matrix A to map l ∞ (Δ) or c(Δ) into l ∞ or c , and investigate related questions.
In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property (β) for this space and also show that it is not rotund where p = (pr) is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ ℕ.
In this paper we introduce and examine some properties of the sequence spaces C(Δvm,θ,(p)),C[Δvm,θ,(p)],C∞(Δvm,θ,(p)),C∞[Δvm,θ,(p)],Nθ(Δvm,(p)),Sθ(Δvm) and study various properties and inclusion relations of these spaces. We also show that the space Sθ(Δvm) may be represented as Nθ(Δvm,(p)) space.
We define a generalized Cesaro sequence space and consider it equipped with the Luxemburg norm under which it is a Banach space, and we show that it is locally uniformly rotund.
Weak convergence of the sequence of the successive approximations for non expansive mappings
Z. Opial, Weak convergence of the sequence of the successive approximations for non
expansive mappings.Bull AmerMath Soc. 73 (1967) 591-597.
A new type of dierence sequence spaces
- B C Tripathy
- A Esi
B. C. Tripathy, A. Esi, A new type of dierence sequence spaces, Int. J. Sci. Technol.
1 (2006), 1114.