scholarly journals Function Polynomization Methods and their Applications

2020 ◽  
Vol 26 (3) ◽  
pp. 437-449
Author(s):  
A. D. Nakhman ◽  
Keyword(s):  
Continuous Functions ◽  
Upper Bounds ◽  
Chebyshev Series ◽  
Space Of Continuous Functions ◽  
Lebesgue Points ◽  
Break Points ◽  
Power Moments

A class of semicontinuous quasiconvex methods of summation of Fourier – Chebyshev series is studied. Upper bounds are obtained for the norms of the corresponding operators in the space of continuous functions. The convergence of means in the metric of space is established. The summability at break points of the first kind is also considered. Processes for restoring functions from a given sequence of power moments are proposed. Ways of generalizing the results and extending them to the case of summability at Lebesgue points are indicated.

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

scholarly journals Generalized Stochastic Dominance: An Empirical Examination

1990 ◽  
Vol 22 (2) ◽  
pp. 49-55 ◽  
Author(s):  
Bruce A. McCarl
Keyword(s):  
Risk Aversion ◽  
Stochastic Dominance ◽  
Upper Bounds ◽  
Information Discovery ◽  
Lower And Upper Bounds ◽  
Empirical Examination ◽  
Data Scaling ◽  
Break Points ◽  
Risk Aversion Coefficient ◽  
Exponential Utility Function

Abstract Use of generalized stochastic dominance (GSD) requires one to place lower and upper bounds on the risk aversion coefficient. This study showed that breakeven risk aversion coefficients found assuming the exponential utility function delineate the places where GSD preferences switch between prospects. However, between these break points, multiple, overlapping GSD intervals can be found. Consequently, when one does not have risk aversion coefficient information, discovery of breakeven coefficients instead of GSD use is recommended. The investigation also showed GSD results are insensitive to wealth and data scaling but are sensitive to rounding.

scholarly journals Korovkin sets for an operator on a space of continuous functions

1976 ◽  
Vol 65 (2) ◽  
pp. 337-345 ◽  
Author(s):  
Le Baron Ferguson ◽  
Michael D. Rusk
Keyword(s):  
Continuous Functions ◽  
Space Of Continuous Functions
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