Banach and Generalized Limits

2021 ◽  
pp. 33-52
Author(s):  
Gokulananda Das ◽  
Sudarsan Nanda
Keyword(s):  
1976 ◽  
Vol 22 (4) ◽  
pp. 446-455 ◽  
Author(s):  
Sudarsan Nanda

AbstractIn this paper we investigate some new sequence spaces which naturally emerge from the concept of almost convergence. Just as ordinary, absolute and strong summability, it is expected that almost convergence must give rise to almost, absolutely almost and strongly almost summability. Almost and absolutely almost summable sequences have been discussed by several authors. The object of this paper is to introduce the spaces of strongly almost summable sequences which happen to be complete paranormed spaces under certain conditions. Some topological results, characterisation of strongly almost regular matrices, uniqueness of generalized limits and inclusion relations of such sequences have been discussed.


2003 ◽  
Vol 21 (2) ◽  
pp. 153-165
Author(s):  
Jeff R. Clark ◽  
Dwight R. Lee

Abstract Special interest groups possess political influence exceeding their size and influence government’s expansion beyond efficiency limits. T h e prisoners’ dilemma illustrates that although it is in the interest of each group to capture maximum government benefits, when all do, all groups are worse off collectively. T h e result is a government that is too large, with gains to each group worth less than their costs. Further gains could be derived if all groups reduce their demands on government. However, securing agreement on such reform is difficult. Unilaterally reducing demands on government means individuals pay for benefits of others without receiving anything in return. Standard discussions of reducing the size of government by overcoming prisoners’ dilemma incentives understate the degree of difficulty involved. We demonstrate that once groups choose noncooperation, they develop skills, which build up over time, thereby enlarging the payoff to the chosen path. As the damage from political rent seeking increases, the motivation for reform declines. However, beyond some point, even with the skill set that has evolved, individual gains from rent seeking are worth less than the costs of the rent-seeking privileges of others. Thus, the prospect of imposing generalized limits on political privileges improves, even though they impose short-run costs.


2015 ◽  
Vol 13 (3) ◽  
pp. 1135-1149 ◽  
Author(s):  
T. Yurdakadim ◽  
M. K. Khan ◽  
H. I. Miller ◽  
C. Orhan

2007 ◽  
Vol 98 (9) ◽  
Author(s):  
Sergio Boixo ◽  
Steven T. Flammia ◽  
Carlton M. Caves ◽  
JM Geremia

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