scholarly journals L0-EMBEDDING OF A LINEAR METRIC SPACE

1979 ◽  
Vol 33 (2) ◽  
pp. 391-398 ◽  
Author(s):  
Yoshiaki OKAZAKI
Keyword(s):  
Metric Space ◽  
Linear Metric Space

Structure of balls and uniqueness subspaces in a linear metric space

1973 ◽  
Vol 13 (4) ◽  
pp. 328-332
Author(s):  
A. I. Vasil'ev
Keyword(s):  
Metric Space ◽  
Linear Metric Space

scholarly journals Continuity of the Solution Maps for Generalized Parametric Set-Valued Ky Fan Inequality Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Z. Y. Peng ◽  
X. B. Li
Keyword(s):  
Metric Space ◽  
Lower Semicontinuity ◽  
Ky Fan Inequality ◽  
Solution Maps ◽  
Linear Metric Space ◽  
Ky Fan ◽  
Upper And Lower Semicontinuity

Under new assumptions, we provide suffcient conditions for the (upper and lower) semicontinuity and continuity of the solution mappings to a class of generalized parametric set-valued Ky Fan inequality problems in linear metric space. These results extend and improve some known results in the literature (e.g., Gong, 2008; Gong and Yoa, 2008; Chen and Gong, 2010; Li and Fang, 2010). Some examples are given to illustrate our results.

Convergence field of Abel’s summation method

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Peter Letavaj
Keyword(s):  
Metric Space ◽  
Linear Subspace ◽  
Summation Method ◽  
Matrix Transformation ◽  
Matrix Transformations ◽  
Regular Matrix ◽  
Porous Set ◽  
Linear Metric Space ◽  
Bounded Sequences

AbstractLet F(A) denote the set of all bounded sequences summable by Abel’s method. It is known, that F(A) is a linear subspace of the linear metric space (S, ρ) of all bounded sequences endowed with the sup metric. It is shown in [KOSTYRKO, P.: Convergence fields of regular matrix transformations 2, Tatra Mt. Math. Publ. 40 (2008), 143–147] that the convergence field of a regular matrix transformation is a σ-porous set. We show that F(A) is very porous in S.

FK Spaces in Which the Sequence of Coordinate Vectors is Bounded

1973 ◽  
Vol 25 (5) ◽  
pp. 973-978 ◽  
Author(s):  
William H. Ruckle
Keyword(s):  
Metric Space ◽  
Complex Sequences ◽  
Linear Metric Space ◽  
Locally Convex

The work presented in this paper was initially motivated by the following question of A. Wilansky: “Is there a smallest FK-space E in which is bounded?” Here FK-space means a complete linear metric space of real or complex sequences x = (xi) upon which the coordinate functional x → xt are continuous for each i (see [10, p. 202]), and An FK-space need not be locally convex, and therein lies the difficulty of the problem since it is easy to see that l1 is the smallest locally convex FK-space.

scholarly journals New type of generalized difference sequence space of non-absolute type and some matrix transformations

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1381-1392 ◽  
Author(s):  
M. Mursaleen ◽  
Ab. Ganie ◽  
Neyaz Sheikh
Keyword(s):  
Sequence Space ◽  
Metric Space ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Difference Matrix ◽  
Riesz Mean ◽  
Difference Sequence Space ◽  
New Type ◽  
Linear Metric Space ◽  
Matrix Class

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 ?-, ?- and ?-duals. Furthermore, we have constructed the basis of rqB(u,p) and characterize a matrix class (rqB(u, p), l?).

scholarly journals Stability of Jungck-type iterative procedures

2005 ◽  
Vol 2005 (19) ◽  
pp. 3035-3043 ◽  
Author(s):  
S. L. Singh ◽  
Charu Bhatnagar ◽  
S. N. Mishra
Keyword(s):  
Metric Space ◽  
Linear Metric Space ◽  
The Stability ◽  
Iterative Procedures

We introduce and discuss the stability of Jungck and Jungck-Mann iterative procedures for a pair of Jungck-Osilike-type maps on an arbitrary set with values in a metric or linear metric space.

Borel sets and the spectrum of an operator on an F-space

1981 ◽  
Vol 90 (3-4) ◽  
pp. 257-261 ◽  
Author(s):  
Zbigniew Słodkowski
Keyword(s):  
Linear Operator ◽  
Metric Space ◽  
Spectrum Of An Operator ◽  
Borel Set ◽  
Borel Sets ◽  
Linear Metric Space ◽  
Locally Convex

SynopsisIt is shown that the spectrum of a linear operator T on a complete linear metric space X is a Borel set. If, in addition, X is locally convex or separable, then the spectrum of T is a Gδσ set.

THE EMBEDDED THEOREM AND ITS APPLICATION TO STATISTICAL METRIC SPACE

1987 ◽  
Vol 7 (3) ◽  
pp. 287-297
Author(s):  
Liu Zhoshu
Keyword(s):  
Metric Space

Generalized multivalued integral type contraction on weak partial metric space

2020 ◽  
Vol 13 (3) ◽  
pp. 145-151
Author(s):  
Öztürk zlem Acar ◽  
Sümeyye Coşkun
Keyword(s):  
Metric Space ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Integral Type ◽  
Type Contraction
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