Series representation of continuous functions

In this paper, we find fractional Riemann–Liouville derivatives for the Takagi–Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi–Landsberg functions, which have arbitrary bounded coefficients in the expansion under Schauder basis. The class of weighted Takagi–Landsberg functions of order H > 0 on [0; 1] coincides with the class of H-Hölder continuous functions on [0; 1]. Based on computed fractional integrals and derivatives of the Haar and Schauder functions, we get a new series representation of the fractional derivatives of a Hölder continuous function. This result allows us to get a new formula of a Riemann–Stieltjes integral. The application of such series representation is a new method of numerical solution of the Volterra and linear integral equations driven by a Hölder continuous function.

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Series representation of flux for the Boussinesq equation

Water Resources Research ◽

10.1029/90wr01696 ◽

1990 ◽

Vol 26 (12) ◽

pp. 2881-2886

Author(s):

P. Tolinkas

Keyword(s):

Boussinesq Equation ◽

Series Representation

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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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A method to obtain sufficient conditions for the stability of a class of internally delayed systems under a Taylor series representation

1992 American Control Conference ◽

10.23919/acc.1992.4792455 ◽

1992 ◽

Author(s):

Carlos F. Alastruey ◽

Manuel De La Sen ◽

Victor Etxebarria

Keyword(s):

Taylor Series ◽

Series Representation ◽

Sufficient Conditions ◽

Delayed Systems ◽

The Stability

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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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