Journal ArticleDOI
Fractal bases for banach spaces of smooth functions
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TLDR
In this paper, the Barnsley-Harrington theorem for differentiability of fractal interpolation functions with variable scaling parameters is extended to the case of smooth fractal functions.Abstract:
This article explores the properties of fractal interpolation functions with variable scaling parameters, in the context of smooth fractal functions. The first part extends the Barnsley–Harrington theorem for differentiability of fractal functions and the fractal analogue of Hermite interpolation to the present setting. The general result is applied on a special class of iterated function systems in order to develop differentiability of the so-called consisting of smooth fractal functions.read more
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A Course In Functional Analysis
TL;DR: A course in functional analysis is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Journal ArticleDOI
Box dimension of α-fractal function with variable scaling factors in subintervals
TL;DR: In this paper, the box dimension of the graph of non-affine α -fractal interpolation function f α with variable scaling factors is estimated in the interval [0, 1].
Journal ArticleDOI
A new class of rational cubic spline fractal interpolation function and its constrained aspects
TL;DR: This paper constructs a new class of rational cubic spline FIFs (RCSFIFs) with a preassigned quadratic denominator with two shape parameters, which includes classical rational cubic interpolant [Appl. Comp., 216 (2010), pp. 2036–2049] as special case and improves the sufficient conditions for positivity.
Journal ArticleDOI
Riemann–Liouville fractional integral of non-affine fractal interpolation function and its fractional operator
T. M. C. Priyanka,A. Gowrisankar +1 more
TL;DR: In this article, the Riemann-Liouville fractional integral of a continuous function with vertical scaling factor as a constant as well as a closed interval of interpolation is investigated.
Journal ArticleDOI
Shape preserving rational quartic fractal functions
TL;DR: The appearance of fractal interpolation function represents a revival of experimental mathematics, raised by computers and intensified by powerful evidence of its applications as mentioned in this paper, and it represents a new direction for experimental mathematics.
References
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Book
Introduction to Numerical Analysis
Josef Stoer,Roland Bulirsch +1 more
TL;DR: This well written book is enlarged by the following topics: B-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for theLR and QR algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations and preconditioning techniques.
Book
Fractals Everywhere
TL;DR: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section.
Book
A Course in Functional Analysis
TL;DR: In this article, an introductory text in functional analysis aimed at the graduate student with a firm background in integration and measure theory is presented, which helps the student to develop an intuitive feel for the subject.
A Course In Functional Analysis
TL;DR: A course in functional analysis is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.