On Müntz Rational Approximation Rate in Lp Spaces

Fractal interpolation function defined with the aid of iterated function system can be employed to show that any continuous real-valued function defined on a compact interval is a special case of a class of fractal functions (self-referential functions). Elements of the iterated function system can be selected appropriately so that the corresponding fractal function enjoys certain properties. In the first part of the paper, we associate a class of self-referential L p -functions with a prescribed L p -function. Further, we apply our construction of fractal functions in L p -spaces in some approximation problems, for instance, to derive fractal versions of the full Müntz theorems in L p -spaces. The second part of the paper is devoted to identify parameters so that the fractal functions affiliated to a given continuous function satisfy certain conditions, which in turn facilitate them to find applications in some one-sided uniform approximation problems.

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“…From [18] we note that under the said hypotheses, the following estimate for Müntz rational approximation rate holds:…”

Section: Proof From Proposition 22 and Remark 21 It Follows Thatmentioning

confidence: 99%

Associate fractal functions inLp-spaces and in one-sided uniform approximation

Viswanathan

Navascués

Chand

2016

Journal of Mathematical Analysis and Applications

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show abstract

“…Rational Müntz Approximation has been researched in [5], shows the application of Theorem 12, and simplifies the proof of [5]. Write…”

Section: Rational Müntz Approximationmentioning

confidence: 99%

“…We verify that ( , ) satisfies all the requirements of Theorem 12. Take Φ( ) = − , where > 0 is the constant appeared in [4], or [5]; see the following inequality (77). Given a fixed with 0 < < 1, we verify that (i) ( 1− ( )) < ∞.…”

Section: Rational Müntz Approximationmentioning

confidence: 99%