ON AFFINE EXTENSIONS OF CONTINUOUS FUNCTIONS DEFINED ON THE EXTREME BOUNDARY OF A CHOQUET SIMPLEX

Abstract This paper concerns the analysis of the structure of bi-contractive projections on spaces of vector valued continuous functions and presents results that extend the characterization of bi-contractive projections given by the first author. It also includes a partial generalization of these results to affine and vector valued continuous functions from a Choquet simplex into a Hilbert space.

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A Choquet-Deny theorem for affine functions on a Choquet simplex

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500012992 ◽

1969 ◽

Vol 16 (4) ◽

pp. 325-327 ◽

Cited By ~ 1

Author(s):

H. A. Priestley

Keyword(s):

Compact Hausdorff Space ◽

Hausdorff Space ◽

Present Note ◽

Continuous Functions ◽

Choquet Simplex ◽

Affine Functions ◽

Stone Theorem

The closed wedges in C(X) (the space of real continuous functions on a compact Hausdorff space X) which are also inf-lattices have been characterized by Choquet and Deny (2); see also (5). The present note extends their result to certain wedges of affine continuous functions on a Choquet simplex, the generalization being in the same spirit as the generalization of the Kakutani- Stone theorem obtained by Edwards in (4).I should like to thank my supervisor, Dr D. A. Edwards, for suggesting this problem and for his subsequent help. I am also grateful to the referee for correcting several slips.

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Proximinal subspaces ofA(K)of finite codimension

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171203212308 ◽

2003 ◽

Vol 2003 (39) ◽

pp. 2501-2505

Author(s):

T. S. S. R. K. Rao

Keyword(s):

Compact Subset ◽

Convex Set ◽

Compact Convex ◽

Continuous Functions ◽

Finite Codimension ◽

Sufficient Condition ◽

Choquet Simplex ◽

Necessary And Sufficient Condition ◽

Compact Convex Set ◽

Necessary And Sufficient

We study an analogue of Garkavi's result on proximinal subspaces ofC(X)of finite codimension in the context of the spaceA(K)of affine continuous functions on a compact convex setK. We give an example to show that a simple-minded analogue of Garkavi's result fails for these spaces. WhenKis a metrizable Choquet simplex, we give a necessary and sufficient condition for a boundary measure to attain its norm onA(K). We also exhibit proximinal subspaces of finite codimension ofA(K)when the measures are supported on a compact subset of the extreme boundary.

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

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.2009.1129 ◽

2010 ◽

Vol 47 (3) ◽

pp. 289-298 ◽

Cited By ~ 2

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.

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Almost Somewhat Near Continuity and Near Regularity

Moroccan Journal of Pure and Applied Analysis ◽

10.2478/mjpaa-2021-0009 ◽

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.

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Approximating Continuous Functions by Iterated Function Systems and Optimization

SSRN Electronic Journal ◽

10.2139/ssrn.616605 ◽

2002 ◽

Author(s):

Davide La Torre ◽

Matteo Rocca

Keyword(s):

Iterated Function Systems ◽

Continuous Functions ◽

Iterated Function

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On existence result of a class of nonlinear integral equation

Filomat ◽

10.2298/fil1711593b ◽

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.

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