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<p>This paper analyzes the convergence and shape-preserving properties of two interpolants: zipper rational cubic splines (RCSs) and rational cubic spline zipper fractal interpolation functions (RCS ZFIFs). A zipper RCS uses cubic/quadratic rational functions with shape parameters and a binary signature vector, while an RCS ZFIF is derived from a zipper RCS through fractal perturbation with appropriate base and scaling functions. We derive sufficient conditions for shape-preserving properties such as positivity, monotonicity, and boundary containment. Theoretical results are validated using examples of shaped interpolation data.</p>

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RATIONAL CUBIC SPLINE ZIPPER FRACTAL FUNCTIONS AND THEIR SHAPE ASPECTS

  • 期刊论文

  • 发表日期：

    2025年2月10日

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  • Vijay,
  • A. K. B. Chand,
  • A. V. Tetenov

摘要

This paper analyzes the convergence and shape-preserving properties of two interpolants: zipper rational cubic splines (RCSs) and rational cubic spline zipper fractal interpolation functions (RCS ZFIFs). A zipper RCS uses cubic/quadratic rational functions with shape parameters and a binary signature vector, while an RCS ZFIF is derived from a zipper RCS through fractal perturbation with appropriate base and scaling functions. We derive sufficient conditions for shape-preserving properties such as positivity, monotonicity, and boundary containment. Theoretical results are validated using examples of shaped interpolation data.