Sublinear functions onR

1975 ◽  
Vol 12 (2-3) ◽  
pp. 200-206 ◽  
Author(s):  
Edgar Berz
Keyword(s):  
Sublinear Functions

scholarly journals Pointwise multiple averages for sublinear functions

2018 ◽  
Vol 40 (6) ◽  
pp. 1594-1618
Author(s):  
SEBASTIÁN DONOSO ◽  
ANDREAS KOUTSOGIANNIS ◽  
WENBO SUN
Keyword(s):  
Large Class ◽  
Explicit Formula ◽  
Pointwise Convergence ◽  
Limit Function ◽  
Invariant Property ◽  
Ergodic Averages ◽  
Order Zero ◽  
Good For ◽  
Sublinear Functions ◽  
Uniquely Ergodic

For any measure-preserving system $(X,{\mathcal{B}},\unicode[STIX]{x1D707},T_{1},\ldots ,T_{d})$ with no commutativity assumptions on the transformations $T_{i},$$1\leq i\leq d,$ we study the pointwise convergence of multiple ergodic averages with iterates of different growth coming from a large class of sublinear functions. This class properly contains important subclasses of Hardy field functions of order zero and of Fejér functions, i.e., tempered functions of order zero. We show that the convergence of the single average, via an invariant property, implies the convergence of the multiple one. We also provide examples of sublinear functions which are, in general, bad for convergence on arbitrary systems, but good for uniquely ergodic systems. The case where the fastest function is linear is addressed as well, and we provide, in all the cases, an explicit formula of the limit function.

Complete Characterizations of Global Optimality for Problems Involving the Pointwise Minimum of Sublinear Functions

1996 ◽  
Vol 6 (2) ◽  
pp. 362-372 ◽  
Author(s):  
B. M. Glover ◽  
Y. Ishizuka ◽  
V. Jeyakumar ◽  
H. D. Tuan
Keyword(s):  
Global Optimality ◽  
Sublinear Functions

Sublinear functions of measures and variational integrals

1964 ◽  
Vol 31 (1) ◽  
pp. 159-178 ◽  
Author(s):  
Casper Goffman ◽  
James Serrin
Keyword(s):  
Variational Integrals ◽  
Sublinear Functions

The formulas for the representation of functions of two variables as a difference of sublinear functions

Optimization ◽  
2018 ◽  
Vol 68 (10) ◽  
pp. 2055-2070
Author(s):  
Jerzy Grzybowski ◽  
Diethard Pallaschke ◽  
Ryszard Urbański
Keyword(s):  
Functions Of Two Variables ◽  
Sublinear Functions

scholarly journals An approximate Hahn-Banach-Lagrange theorem

2016 ◽  
Vol 19 (4) ◽  
pp. 169-177
Author(s):  
Dinh Nguyen ◽  
Mo Hong Tran
Keyword(s):  
Original Version ◽  
Extended Version ◽  
General Picture ◽  
Farkas Lemma ◽  
Sandwich Theorem ◽  
Banach Theorem ◽  
Special Cases ◽  
Lagrange Theorem ◽  
Sublinear Functions ◽  
Asymptotic Forms

In this paper, we proved a new extended version of the Hahn-Banach-Lagrange theorem that is valid in the absence of a qualification condition and is called an approximate Hahn-Banach-Lagrange theorem. This result, in special cases, gives rise to approximate sandwich and approximate Hahn-Banach theorems. These results extend the Hahn-Banach-Lagrange theorem, the sandwich theorem in [18], and the celebrated Hahn-Banach theorem. The mentioned results extend the original ones into two features: Firstly, they extend the original versions to the case with extended sublinear functions (i.e., the sublinear functions that possibly possess extended real values). Secondly, they are topological versions which held without any qualification condition. Next, we showed that our approximate Hahn-Banach-Lagrange theorem was actually equivalent to the asymptotic Farkas-type results that were established recently [10]. This result, together with the results [5, 16], give us a general picture on the equivalence of the Farkas lemma and the Hahn-Banach theorem, from the original version to their corresponding extensions and in either non-asymptotic or asymptotic forms.

scholarly journals Some remarks on the space of differences of sublinear functions

1994 ◽  
Vol 22 (3) ◽  
pp. 419-426 ◽  
Author(s):  
Sven Bartels ◽  
Diethard Pallaschke
Keyword(s):  
Sublinear Functions
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