scholarly journals Ergodic Optimization of Prevalent Super-continuous Functions

2015 ◽  
Vol 2016 (19) ◽  
pp. 5988-6017 ◽  
Author(s):  
Jairo Bochi ◽  
Yiwei Zhang
Keyword(s):  
Continuous Functions ◽  
Ergodic Optimization

Ergodic optimization of super-continuous functions on shift spaces

2011 ◽  
Vol 32 (6) ◽  
pp. 2071-2082 ◽  
Author(s):  
ANTHONY QUAS ◽  
JASON SIEFKEN
Keyword(s):  
Periodic Orbit ◽  
Dense Subset ◽  
Continuous Functions ◽  
Probability Measures ◽  
Open Dense Subset ◽  
Separable Space ◽  
Ergodic Optimization ◽  
Full Shift ◽  
Separable Spaces ◽  
Positive Results

AbstractErgodic optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that ‘most’ functions are optimized by measures supported on a periodic orbit, and it has been proved in several separable spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. All known positive results have been for separable spaces. We give in this paper the first positive result for a non-separable space, the space of super-continuous functions on the full shift, where the set of functions optimized by periodic orbit measures contains an open dense subset.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

ON ε-CONTINUOUS FUNCTIONS

1995 ◽  
Vol 21 (1) ◽  
pp. 203
Author(s):  
Banaszewski
Keyword(s):  
Continuous Functions

ON THREADING CONTINUOUS FUNCTIONS THROUGH COMPACT SETS

1982 ◽  
Vol 8 (2) ◽  
pp. 455
Author(s):  
Akemann ◽  
Bruckner
Keyword(s):  
Continuous Functions ◽  
Compact Sets

I-density Continuous Functions

1989 ◽  
Vol 15 (1) ◽  
pp. 13
Author(s):  
Ciesielski ◽  
Larson ◽  
Ostaszewski
Keyword(s):  
Continuous Functions
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