On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures

被引：0
|
作者：
Rattan Lal
Bilel Selmi
Saurabh Verma
机构：
[1] Deemed to be University,Department of Mathematics, Punjab Engineering College
[2] University of Monastir,Analysis, Probability and Fractals Laboratory: LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir
[3] IIIT Allahabad,Department of Applied Sciences
来源：
Results in Mathematics | 2024年 / 79卷
关键词：
fractal dimensions; fractal interpolation; Sierpiński gasket; Hölder continuous; invariant measures; 28A12; 28A25; 28A78; 28A80; 28C20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this article, our aim is to estimate the fractal dimensions of the graphs of fractal interpolation functions (FIFs) on the product of two Sierpiński gaskets. To achieve this, we employ the Hölder function spaces. We also define a fractal operator on Hölder spaces originated from the FIFs and establish some operator-theoretic properties such as bounded below and invariant subspaces of it. Additionally, we provide bounds on the Hausdorff dimensions of the invariant measures that are supported on the graphs of these FIFs.
引用
收藏
相关论文
共 50 条
  • [1] On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures
    Lal, Rattan
    Selmi, Bilel
    Verma, Saurabh
    RESULTS IN MATHEMATICS, 2024, 79 (02)
  • [2] OSCILLATION AND DIMENSIONS OF HARMONIC FUNCTIONS ON THE SIERPIŃSKI GASKETS
    Liang, Zhen
    Ruan, Huo-jun
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2024,
  • [3] Non-Stationary Fractal Functions on the Sierpiński Gasket
    Kumar, Anuj
    Boulaaras, Salah
    Verma, Shubham Kumar
    Biomy, Mohamed
    MATHEMATICS, 2024, 12 (22)
  • [4] Geodesics of right isosceles Sierpiński gaskets and their relatives
    Li, Xiaohan
    Liang, Xiangyu
    Xue, Yumei
    CHAOS SOLITONS & FRACTALS, 2025, 192
  • [5] Wave functions in the critical phase: A planar Sierpiński fractal lattice
    Yao, Qi
    Yang, Xiaotian
    Iliasov, Askar A.
    Katsnelson, Mikhail I.
    Yuan, Shengjun
    PHYSICAL REVIEW B, 2024, 110 (03)
  • [6] Analytical and dimensional properties of fractal interpolation functions on the Sierpiński gasket
    Manuj Verma
    Amit Priyadarshi
    Saurabh Verma
    Fractional Calculus and Applied Analysis, 2023, 26 : 1294 - 1325
  • [7] The Sierpi?ski product of graphs
    Kovic, Jurij
    Pisanski, Tomaz
    Zemljic, Sara Sabrina
    Zitnik, Arjana
    ARS MATHEMATICA CONTEMPORANEA, 2023, 23 (01)
  • [8] The quantization dimension of the self-affine measures on general Sierpiński carpets
    Sanguo Zhu
    Monatshefte für Mathematik, 2011, 162 : 355 - 374
  • [9] Concerning the Vector-Valued Fractal Interpolation Functions on the Sierpiński Gasket
    M. A. Navascués
    S. Verma
    P. Viswanathan
    Mediterranean Journal of Mathematics, 2021, 18
  • [10] Propagating Sets in Sierpiński Fractal Graphs
    Anitha, J.
    Rajasingh, Indra
    Rashmanlou, Hossein
    RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS, 2025, 59
12345