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Tuesday, October 13, 2020 | History

2 edition of Modulared semi-ordered linear spaces found in the catalog.

Modulared semi-ordered linear spaces

HidegoroМ‚ Nakano

# Modulared semi-ordered linear spaces

## by HidegoroМ‚ Nakano

• 150 Want to read
• 27 Currently reading

Written in English

Subjects:
• Linear topological spaces.

• Edition Notes

The Physical Object ID Numbers Statement by Hidegorô Nakano. Series Tokyo mathematical book series -- v.1 Pagination 288p. ; Number of Pages 288 Open Library OL21488504M

Modular space, K-modular space, F-modular space References [1] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debre 31 . [1] M. Abbas, B. E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type, Fixed Point Theory Appl. (),

In a modular space, we introduce the concept of a best approximation and prove results about proximinal set, Chebysev set and existence invariant best approximation. Keywords Modular spaces, best approximation, fixed points. AMS () subject classification: 46B20, 47H 1-INTRODUCTION. for all λ > 0 which implies that lim n → ∞ y n = x *.. Theorem Let w be a metric modular on X and X w be a modular metric space induced by w. If X w is a complete modular metric space and T: X w → X w is a mapping, which T N is a contraction mapping for some positive integer N. Then, T has a unique fixed point in X w.. Theorem , T N has a unique fixed point u ∈ X w.

[1] E. Asplund, Fréchet differentiability of convex functions, Acta Math. (), pp. [2] E. Asplund, and R. T. Rockafellar, Gradients of convex functions.   In this paper a generalization of a modular metric which is also a generalization of cone metric, is introduced and some of its topological properties are studied. Next, a fixed point theorem in this space is proved and finally by an example, it is proved that the fixed point result of the paper "Ch. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mapping in.

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### Modulared semi-ordered linear spaces by HidegoroМ‚ Nakano Download PDF EPUB FB2

Modulared semi-ordered linear spaces (Tokyo mathematical book series) Hardcover – January 1, by HidegoroÌ Nakano (Author) See all formats and editions Hide other formats and editions.

Price New from Used from Hardcover, January 1, "Please retry" — — — Hardcover Author: HidegoroÌ Nakano. The theory of modulared semi-ordered linear spaces have been discussed by H.

Nakano ヰヰヲ as the abstract theory of a function spaces inclu- ding Orlicz spaces 的 andLp-spaces， and also discussed by many others. Tokyo mathematical book series. File: PDF, MB. Reviews. There are no reviews yet. Be the first to review “[PDF] – Modulared semi-ordered linear spaces Ebook” Cancel reply.

in modulared linear spaces without semi-ordering. But, it is our cherished $0\overline{p}inion$ that the semi-ordered linear space is most suitable thefor develop-ment of modular theory, and the opinion has been testiﬁed enough the book: in NAKANO [7], to which we owe the terminology and proper-ties of modulars used in this paper.

(The Cited by: 3. On Normed Spaces and Modulared Semi-ordered Linear Spaces. MODULARED LINEAR SPACE By Sh\={o}z\={o} KOSHI \S 1.

Preliminary. Modulared linear spaces with order structure in which there are functionals called modulars were discussed by H. NAKANO in his book [3]. NAKANO studied these spaces through the properties of these functionals. Above all he deﬁned the uniform properties such as ”uniformly. Musielak, Orlicz Spaces and Modular Spaces, volume of Lecture Notes in Mathematics (Springer, Berlin, ) Google Scholar H.

Nakano, Modulared Semi-Ordered Linear Spaces (Maruzen Co. Ltd., Tokyo, ) zbMATH Google Scholar. ulared Semi-ordered Linear Spaces" he developed his theory of modulared semi-ordered linear space, the so-called Orlicz{Nakano spaces, in full details.

Every-thing was written in abstract form and no concrete examples were presented. Beside the elementary seminar for training, we joined the seminar of the re-search group conducted by Prof. Nakano.

PDF | In the present paper a concept of \$$C^*\$$-algebra-valued modular space is introduced which is a generalization of a modular space.

Next, some | Find, read and cite all the research you. [13] H. NAKANO, Modulared Semi-Ordered Linear Spaces, Tokyo Math. Book Ser, Vol. 1 Maruzen Co, Tokyo (). [14] J.M. RASSIAS,On the stability of the Euler–Lagrange functional equation, Chinese J. Math. 20 no.

2 (), – of quadratic mappings in modular spaces without. Abstract. We prove the continuity in norm of the translation operator in the Musielak-Orlicz L M spaces.

An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in L M, in both the modular and norm density results are then applied to obtain basic topological properties.

Here is a list of books, notes, and theses, meant to be reasonably complete at the time of writing, that contain material on general partially ordered vector spaces and their operators (there is much more on Riesz spaces and their operators), and on topologies as related to ordering (also for Riesz spaces): Nakano, Modulared semi-ordered.

The theory of modulars on linear spaces and the corresponding theory of modular linear spaces were founded by Nakano [1, 2].The attempt to generalize the notion of a modular to avoid its restriction on a linear space or on a space with additional algebraic structure resulted in defining and developing a new modular which works on an arbitrary set.

Lozanovsky’s Note-books (Part I) Membership: none. US$US$ 0. 23 Sep Modulared semi-ordered linear spaces. in Mathematics-Functional Analysis. Add. US$US$%. Modulared semi-ordered linear spaces. Membership: none. US$US$ 3. The notion of modular spaces, as a generalize of metric spaces, was introduced by Nakano and redefined by Musielak and Orlicz.

A lot of mathematicians are interested, fixed points of Modular spaces, for example [15–22]. InRazani and Moradi studied fixed point theorems for -compatible maps of integral type in modular spaces.

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate the existence of fixed points of modular contractive mappings in modular metric spaces.

These are related to the successive approximations of fixed points (via orbits) which. formula for the Mazur-Orlicz F-norm, remains valid in any modular space X, = {x E X: p(Xx) + 0 as X -+ O+}, where X is an abstract linear space and p.

The aim of this paper is to generalize the F -contractive condition in the framework of α − ν-complete modular b-metric spaces. Some results in ordered modular b-metric spaces are also presented.

Moreover, an illustrative example and some related applications. Recall that the theory of modular on linear spaces and the corresponding theory of modular linear spaces were Modulared Semi-Ordered Linear Spaces, vol.

1 of Tokyo Mathematical Book Series, Maruzen, Tokyo, Japan, View at: MathSciNet; H. Nakano, Topology of Linear Topological Spaces, vol. 3 of Tokyo Mathematical Book Series, Maruzen. In this paper, we study an iteration process introduced by Thakur et al.

for Suzuki mappings in Banach spaces, in the new context of modular vector spaces. We establish existence results for a more recent version of Suzuki generalized non-expansive mappings. The stability and data dependence of the scheme for ρ -contractions is studied as well.

Criteria for strict monotonicity, lower local uniform monotonicity, upper local uniform monotonicity and uniform monotonicity of a Musielak–Orlicz space endowed with the Amemiya norm and its subspace of order continuous elements are given in the cases of nonatomic and the counting measure space.

Theorem A (or Orlicz result in Remark 1) and Theorem 2, that is the Amemiya type formula for the Luxemburg norm and also the corresponding formula for the Mazur-Orlicz F-norm, remains valid in any modular space Xp = {x E X: p(Ax) --+ 0 as k --+ 0+}, where X is an abstract linear space and p is either a convex (or s-convex) modular on X or only.You can write a book review and share your experiences.

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