compact convergence
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2015 ◽  
Vol 15 (2) ◽  
pp. 203-212 ◽  
Author(s):  
Ru Liu ◽  
Miao Li ◽  
Sergey Piskarev

AbstractThe semidiscretization methods for solving the Cauchy problem $(\mathbf {D}_{t}^{\alpha }u)(t) = A u(t) + J^{1-\alpha } f\big (t,u(t)\big ), \quad t \in [0,T], 0 < \alpha <1,\qquad u(0) = u^0,$ with operator A, which generates an analytic and compact resolution family ${\lbrace S_{\alpha }(t,A)\rbrace _{t\ge 0}}$, in a Banach space E are presented. It is proved that the compact convergence of resolvents implies the convergence of semidiscrete approximations to an exact solution. We give an analysis of a general approximation scheme, which includes finite differences and projective methods.


2014 ◽  
Vol 278 (3-4) ◽  
pp. 795-827 ◽  
Author(s):  
Mathieu Carette ◽  
Dennis Dreesen

2013 ◽  
Vol 45 (2) ◽  
pp. 600-638 ◽  
Author(s):  
A. N. Carvalho ◽  
J. W. Cholewa ◽  
G. Lozada-Cruz ◽  
M. R. T. Primo

2000 ◽  
Vol 23 (12) ◽  
pp. 849-854
Author(s):  
Phoebe Ho ◽  
Shing S. So

Clifford and Preston (1961) showed several important characterizations of right groups. It was shown in Roy and So (1998) that, among topological semigroups, compact right simple or left cancellative semigroups are in fact right groups, and the closure of a right simple subsemigroup of a compact semigroup is always a right subgroup. In this paper, it is shown that such results can be generalized in convergence semigroups. In the discussion of maximal right simple subsemigroups and maximal right subgroups of semigroups, generalization of the results that no two maximal right simple subsemigroups and maximal right subgroups of a convergence semigroup intersect, is also established.


1998 ◽  
Vol 21 (1) ◽  
pp. 153-157
Author(s):  
Phoebe Ho ◽  
Paul Plummer ◽  
Shing So
Keyword(s):  

In this paper the concept of convergence defined by filters is used and applied in the study of semigroups. Special emphasis is placed on compact convergence semigroups and their properties.


1993 ◽  
Vol 16 (1) ◽  
pp. 101-109 ◽  
Author(s):  
S. Kundu ◽  
R. A. McCoy

This paper studies two topologies on the set of all continuous real-valued functions on a Tychonoff space which lie between the topologies of compact convergence and uniform convergence.


1983 ◽  
Vol 26 (2) ◽  
pp. 179-188 ◽  
Author(s):  
Ludwig Tomm

AbstractIn this paper an explicit regular sequence-to-sequence summability method is presented which sums the geometric series to the value 1/(1-z) in all of ℂ\{1} and to infinity at the point 1. The method also provides compact convergence in ℂ \ [ 1, ∞) and therefore improves well-known results by Le Roy, Lindelöf and Mittag-Leffler.


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