Applications of the Hahn-Banach theorem and dual extremal problems

1971 ◽  
pp. 68-80
Author(s):  
Harold S. Shapiro
Keyword(s):  
Extremal Problems ◽  
Banach Theorem

Some Extremal Problems in (D, D+1)-Regular Graphs

2016 ◽  
Vol 6 (2) ◽  
pp. 105
Author(s):  
N. Murugesan ◽  
R. Anitha
Keyword(s):  
Extremal Problems ◽  
Regular Graphs

scholarly journals Strong submeasures and applications to non-compact dynamical systems

2020 ◽  
pp. 1-23
Author(s):  
TUYEN TRUNG TRUONG
Keyword(s):  
Metric Space ◽  
Bounded Operator ◽  
Continuous Functions ◽  
Open Dense Subset ◽  
Compact Metric Space ◽  
Basic Properties ◽  
Banach Theorem ◽  
Complex Varieties ◽  
Definition Of ◽  
Meromorphic Maps

Abstract A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By the Hahn–Banach theorem, a positive strong submeasure is the supremum of a non-empty collection of measures whose masses are uniformly bounded from above. There are many natural examples of continuous maps of the form $f:U\rightarrow X$ , where X is a compact metric space and $U\subset X$ is an open-dense subset, where f cannot extend to a reasonable function on X. We can mention cases such as transcendental maps of $\mathbb {C}$ , meromorphic maps on compact complex varieties, or continuous self-maps $f:U\rightarrow U$ of a dense open subset $U\subset X$ where X is a compact metric space. For the aforementioned mentioned the use of measures is not sufficient to establish the basic properties of ergodic theory, such as the existence of invariant measures or a reasonable definition of measure-theoretic entropy and topological entropy. In this paper we show that strong submeasures can be used to completely resolve the issue and establish these basic properties. In another paper we apply strong submeasures to the intersection of positive closed $(1,1)$ currents on compact Kähler manifolds.

Extremal Problems Involving the Two Largest Complementarity Eigenvalues of a Graph

2019 ◽  
Vol 36 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Alberto Seeger ◽  
David Sossa
Keyword(s):  
Extremal Problems

Some extremal problems for circular polygons

1996 ◽  
Vol 80 (4) ◽  
pp. 1956-1961
Author(s):  
A. Yu. Solynin
Keyword(s):  
Extremal Problems

Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Małgorzata Klimek ◽  
Marek Błasik
Keyword(s):  
Differential Equations ◽  
Arbitrary Order ◽  
Continuous Solution ◽  
Initial Value ◽  
Uniqueness Results ◽  
Banach Theorem ◽  
Arbitrary Partition ◽  
Particular Solution ◽  
Stationary Function ◽  
Fractional Differential

AbstractTwo-term semi-linear and two-term nonlinear fractional differential equations (FDEs) with sequential Caputo derivatives are considered. A unique continuous solution is derived using the equivalent norms/metrics method and the Banach theorem on a fixed point. Both, the unique general solution connected to the stationary function of the highest order derivative and the unique particular solution generated by the initial value problem, are explicitly constructed and proven to exist in an arbitrary interval, provided the nonlinear terms fulfil the corresponding Lipschitz condition. The existence-uniqueness results are given for an arbitrary order of the FDE and an arbitrary partition of orders between the components of sequential derivatives.

Left amenability and left contractibility of Lau algebras

2014 ◽  
Vol 51 (3) ◽  
pp. 407-427
Author(s):  
Ali Jabbari
Keyword(s):  
Topological Semigroups ◽  
Banach Theorem

In this paper we study left amenability of Lau algebras by introducing left approximate diagonal and virtual diagonal for Lau algebras. Some results related to Hahn-Banach theorem property on foundation topological semigroups are obtained. We introduce the left contractibility of Lau algebras. Some examples for clarifying that left contractibility of Lau algebras is stronger than left amenability of them are given.

Some extremal problems on classes of summable functions

1972 ◽  
Vol 24 (5) ◽  
pp. 574-578
Author(s):  
L. G. Khomutenko
Keyword(s):  
Extremal Problems
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