linear metric space
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Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2243
Author(s):  
Yaroslav Bazaykin ◽  
Dušan Bednařík ◽  
Veronika Borůvková ◽  
Tomáš Zuščák

The aim of the paper is to generalize results by Sikorska on some functional equations for set-valued functions. In the paper, a tool is described for solving a generalized type of an integral-functional equation for a set-valued function F:X→cc(Y), where X is a real vector space and Y is a locally convex real linear metric space with an invariant metric. Most general results are described in the case of a compact topological group G equipped with the right-invariant Haar measure acting on X. Further results are found if the group G is finite or Y is Asplund space. The main results are applied to an example where X=R2 and Y=Rn, n∈N, and G is the unitary group U(1).


Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1381-1392 ◽  
Author(s):  
M. Mursaleen ◽  
Ab. Ganie ◽  
Neyaz Sheikh

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?).


2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Z. Y. Peng ◽  
X. B. Li

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.


2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Peter Letavaj

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.


2005 ◽  
Vol 2005 (19) ◽  
pp. 3035-3043 ◽  
Author(s):  
S. L. Singh ◽  
Charu Bhatnagar ◽  
S. N. Mishra

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.


Author(s):  
Zbigniew Słodkowski

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.


1973 ◽  
Vol 25 (5) ◽  
pp. 973-978 ◽  
Author(s):  
William H. Ruckle

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.


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