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

• Published in: Journal of mathematical analysis and applications Vol. 433; no. 2; pp. 862 - 876
• Main Authors: Viswanathan, P., Navascués, M.A., Chand, A.K.B.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.01.2016
• Subjects: [formula omitted]-spaces; Best one-sided approximation; Fractal functions; One-sided uniform approximation; Fractal functions; Best one-sided approximation; Lp-spaces; One-sided uniform approximation
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2015.08.012

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 Lp-functions with a prescribed Lp-function. Further, we apply our construction of fractal functions in Lp-spaces in some approximation problems, for instance, to derive fractal versions of the full Müntz theorems in Lp-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. •Fractal functions in Lp-spaces are investigated in detail.•Fractal versions of the full Müntz theorems in Lp-spaces are derived.•One-sided approximation with fractal functions is broached.•Overall, the article is a step forward in the theory of fractal approximation.