scholarly journals On strictly convex and strictly2-convex2-normed spaces II

1992 ◽  
Vol 15 (3) ◽  
pp. 417-423
Author(s):  
C.-S. Lin
Keyword(s):  
Normed Space ◽  
Duality Mapping ◽  
Normed Spaces ◽  
Strictly Convex ◽  
Different Types

In this paper a new duality mapping is defined, and it is our object to show that there is a similarity among these three types of characterizations of a strictly convex2-normed space. This enables us to obtain more new results along each of two types of characterizations. We shall also investigate a strictly2-convex2-normed space in terms of the above two different types.

scholarly journals Orthogonality in smooth countably normed spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Tawfeek ◽  
Nashat Faried ◽  
H. A. El-Sharkawy
Keyword(s):  
Normed Space ◽  
Nonempty Subset ◽  
Metric Projection ◽  
Orthogonal Complement ◽  
Duality Mapping ◽  
Dual Cone ◽  
Birkhoff Orthogonality ◽  
Uniformly Convex ◽  
Normed Spaces ◽  
Normalized Duality Mapping

AbstractWe generalize the concepts of normalized duality mapping, J-orthogonality and Birkhoff orthogonality from normed spaces to smooth countably normed spaces. We give some basic properties of J-orthogonality in smooth countably normed spaces and show a relation between J-orthogonality and metric projection on smooth uniformly convex complete countably normed spaces. Moreover, we define the J-dual cone and J-orthogonal complement on a nonempty subset S of a smooth countably normed space and prove some basic results about the J-dual cone and the J-orthogonal complement of S.

scholarly journals On normed spaces with the Wigner Property

2019 ◽  
Vol 11 (3) ◽  
pp. 523-539 ◽  
Author(s):  
Ruidong Wang ◽  
Dariusz Bugajewski
Keyword(s):  
Normed Space ◽  
Two Dimensional ◽  
Normed Spaces ◽  
Strictly Convex ◽  
Real Normed Space

AbstractThe aim of this paper is to generalize the Wigner Theorem to real normed spaces. A normed space is said to have the Wigner Property if the Wigner Theorem holds for it. We prove that every two-dimensional real normed space has the Wigner Property. We also study the Wigner Property of real normed spaces of dimension at least three. It is also shown that strictly convex real normed spaces possess the Wigner Property.

scholarly journals On the Mazur-Ulam Theorem in Non-Archimedean Fuzzy -Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Tian Zhou Xu
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Strictly Convex ◽  
Ulam Theorem

The motivation of this paper is to present a new notion of non-Archimedean fuzzy -normed space over a field with valuation. We obtain a Mazur-Ulam theorem for fuzzy -isometry mappings in the strictly convex non-Archimedean fuzzy -normed spaces. We also prove that the interior preserving mapping carries the barycenter of a triangle to the barycenter point of the corresponding triangle. And then, using this result, we get a Mazur-Ulam theorem for the interior preserving fuzzy -isometry mappings in non-Archimedean fuzzy -normed spaces over a linear ordered non-Archimedean field.

scholarly journals Ideal Convergence and Completeness of a Normed Space

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 897 ◽  
Author(s):  
Fernando León-Saavedra ◽  
Francisco Javier Pérez-Fernández ◽  
María del Pilar Romero de la Rosa ◽  
Antonio Sala
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Convergence Space ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Underlying Space ◽  
Phd Thesis

We aim to unify several results which characterize when a series is weakly unconditionally Cauchy (wuc) in terms of the completeness of a convergence space associated to the wuc series. If, additionally, the space is completed for each wuc series, then the underlying space is complete. In the process the existing proofs are simplified and some unanswered questions are solved. This research line was originated in the PhD thesis of the second author. Since then, it has been possible to characterize the completeness of a normed spaces through different convergence subspaces (which are be defined using different kinds of convergence) associated to an unconditionally Cauchy sequence.

Some sequence spaces and completeness of normed spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 281-287
Author(s):  
RAMAZAN KAMA ◽  
◽  
BILAL ALTAY ◽  
Keyword(s):  
Normed Space ◽  
Summability Method ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Cesàro Summability ◽  
Cesaro Summability

In this paper we introduce new sequence spaces obtained by series in normed spaces and Cesaro summability method. We prove that completeness ´ and barrelledness of a normed space can be characterized by means of these sequence spaces. Also we establish some inclusion relationships associated with the aforementioned sequence spaces.

scholarly journals Strongly Lacunary Ward Continuity in 2-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hüseyin Çakalli ◽  
Sibel Ersan
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Cauchy Sequences

A functionfdefined on a subsetEof a 2-normed spaceXis strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points inE; that is,(f(xk))is a strongly lacunary quasi-Cauchy sequence whenever (xk) is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in 2-normed spaces.

scholarly journals Isometries of ultrametric normed spaces

2021 ◽  
Vol 12 (4) ◽  
Author(s):  
Javier Cabello Sánchez ◽  
José Navarro Garmendia
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Tingley’S Problem ◽  
Group Of Isometries

AbstractWe show that the group of isometries of an ultrametric normed space can be seen as a kind of a fractal. Then, we apply this description to study ultrametric counterparts of some classical problems in Archimedean analysis, such as the so called Problème des rotations de Mazur or Tingley’s problem. In particular, it turns out that, in contrast with the case of real normed spaces, isometries between ultrametric normed spaces can be very far from being linear.

scholarly journals Some properties of the superior and inferior semi inner product function associated to the 2-norm

2016 ◽  
Vol 12 (5) ◽  
pp. 6254-6260
Author(s):  
Stela Ceno
Keyword(s):  
Normed Space ◽  
Scalar Product ◽  
Inner Product ◽  
Normed Spaces ◽  
Close Link ◽  
Long Period ◽  
Product Function

Special properties that the scalar product enjoys and its close link with the norm function have raised the interest of researchers from a very long period of time. S.S. Dragomir  presents concrete generalizations of the scalar product functions  in a normed space and deals with the interesting properties of them. Based on S.S. Dragomirs idea in this paper we treat generalizations of superior and inferior scalar product functions in the case of semi-normed spaces and 2-normed spaces.

scholarly journals Some fixed point theorems in n-normed spaces

2020 ◽  
Vol 25 (3) ◽  
pp. 1-15 ◽  
Author(s):  
Hanan Sabah Lazam ◽  
Salwa Salman Abed
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Normed Space ◽  
Fixed Point Theorems ◽  
Normed Spaces ◽  
Weak Contraction ◽  
Contraction Mappings ◽  
Basic Properties ◽  
Definition Of

In this article, we recall the definition of a real n-normed space and some basic properties. fixed point theorems for types of Kannan, Chatterge, Zamfirescu, -Weak contraction and  - (,)-Weak contraction mappings in  Banach spaces.

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