On differentiability properties of typical continuous functions and Haar null sets

AbstractWe characterize the pairs of weights (v, w) for which the operator with s and h increasing and continuous functions is of strong type (p, q) or weak type (p, q) with respect to the pair (v, w) in the case 0 < q < p and 1 < p < ∞. The result for the weak type is new while the characterizations for the strong type improve the ones given by H. P. Heinig and G. Sinnamon. In particular, we do not assume differentiability properties on s and h and we obtain that the strong type inequality (p, q), q < p, is characterized by the fact that the functionbelongs to Lr(gqw), where 1/r = 1/q – 1/p and the supremum is taken over all c and d such that c ≤ x ≤ d and s(d) ≤ h(c).

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DIFFERENTIABILITY PROPERTIES OF TYPICAL CONTINUOUS FUNCTIONS

Real Analysis Exchange ◽

10.2307/44153061 ◽

1999 ◽

Vol 25 (1) ◽

pp. 149

Author(s):

Zajíček

Keyword(s):

Continuous Functions ◽

Differentiability Properties

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NONDIFFERENTIABILITY PROPERTIES OF TYPICAL CONTINUOUS FUNCTIONS, POROUS SETS, AND HAAR NULL SETS

Real Analysis Exchange ◽

10.2307/44153019 ◽

1999 ◽

Vol 25 (1) ◽

pp. 19

Author(s):

Kolář

Keyword(s):

Continuous Functions ◽

Haar Null Sets ◽

Porous Sets

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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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