과제정보
The first author gratefully acknowledges the financial support of the Council of Scientific and Industrial Research, India (CSIR).
참고문헌
- R.K. Aswathy, S. Mathew, On different forms of self similarity, Chaos, Solitons and Fractals 87 (2016), 102-108.
- R.K. Aswathy, S. Mathew, Separation properties of finite products of hyperbolic iterated function systems, Communications in Nonlinear Science and Numerical Simulation 67 (2019), 594-599.
- R.K. Aswathy, S. Mathew, Weak self similar sets in separable metric spaces, Fractals 25 (2017), 1750021.
- R. Balu, S. Mathew, On (n, m)-Iterated Function System, Asian-European Journal of Mathematics 6 (2013), 1350055.
- R. Balu, S. Mathew, N.A. Secelean, Separation properties of (n, m)-IFS attractors, Communications in Nonlinear Science and Numerical Simulation 51 (2017), 160-168.
- C. Bandt, Self-similar sets 5. Integer matrices and fractal tilings of Rn, Proceedings of the American Mathematical Society 112 (1991), 549-562.
- C. Bandt, S. Graf, Self-similar sets 7. A characterization of self-similar fractals with positive Hausdorff measure, Proceedings of the American Mathematical Society (1992), 995-1001.
- M.F. Barnsley, Fractals everywhere, Academic press 2014.
- P.F. Duvall, L.S. Husch, Attractors of iterated function systems, Proceedings of the American Mathematical Society 116 (1992), 279-284.
- K.J. Falconer, Fractal geometry: Mathematical foundations and applications, John Wiley and Sons, New York, 1990.
- K.J. Falconer, Sub self similar sets, Transactions of the American Mathematical Society 347 (1995), 3121-3129.
- A. Garg, A. Negi, A. Agrawal, B. Latwal, Geometric Modelling Of Complex Objects Using Iterated Function System, International Journal of International Journal of Scientific and Technology Research 3 (2014), 1-8.
- M. Hata, On the structure of self-similar sets, Japan Journal of Applied Mathematics 2 (1985), 381-414.
- R. Hohlfeld, N. Cohen, Self-similarity and the geometric requirements for frequency independence in antennae, Fractals 7 (1999), 79-84.
- A. Husain, M.N. Nanda, M.S. Chowdary, M. Sajid, Fractals: An Eclectic Survey, Part I, Fractal and Fractional 6(2022), 89.
- A. Husain, M.N. Nanda, M.S. Chowdary, M. Sajid, Fractals: An Eclectic Survey, Part II, Fractal and Fractional 6 (2022), 379.
- J.E. Hutchinson, Fractals and self similarity, Indiana University Mathematics Journal 30 (1981), 713-747.
- K.D. Joshi, Introduction to general topology, New Age International, 1983.
- B. Mandelbrot, The fractal geometry of nature, WH Freeman, New York, 1982.
- P. Mattila, On the structure of self-similar fractals, Annales Academire Scientiarum Fennicrc. Series A. I. Mathematica 7 (1982), 189-195.
- M. McClure, The Boral structure of the collections of sub self similar sets and super self similar sets, Acta Mathematics Universitatis Comenianae LXIX (2000), 145-149.
- S. Minirani, S. Mathew, Fractals in Partial Metric spaces, Fractals, Wavelets and its Applications 92 (2014), 203-215.
- S. Minirani, S. Mathew, On topology of fractal space, Mathematical Sciences International Research Journal 2 (2012), 262-275.
- J.R. Munkres, Topology, Prentice Hall, US, 2000.
- N. Niralda, S. Mathew, N.A. Secelean, On boundaries of attractors in dynamical systems, Communications in Non Linear Science and Numerical Simulation 94 (2021), 105572.
- B. Rama, J. Mishra, Generation of 3D Fractal Images for Mandelbrot and Julia Sets, International Journal of Computer and Communication Technology 1 (2010), 178-182.
- F. Sandoghdar, Connectedness of the attractor of an iterated function system, Concordia University, 1995.
- A.J. Sayooj, R. Raja, B.I. Omede, R.P. Agarwal, J. Cao, V.E. Balas, Mathematical Modeling on Co-infection: Transmission Dynamics of Zika virus and Dengue fever, Nonlinear Dynamics 111 (2023), 4879-4914.
- A. Schief, Self-similar sets in complete metric spaces, Proceedings of the American Mathematical Society 124 (1996), 481-490.
- A. Schief, Separation properties for self-similar sets, Proceedings of the American Mathematical Society 122 (1994), 111-115.
- N.A. Secelean, Countable iterated function systems, Far East Journal of Dynamical Systems 3 (2001), 149-167.
- N.A. Secelean, Generalized countable iterated function systems, Filomat 25 (2011), 21-36.
- N.A. Secelean, Generalized countable iterated function systems on the space l∞(x), Journal of Mathematical Analysis and Applications 410 (2014), 847-858.
- N.A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory and Application 1 (2013), 1-13.
- N.A. Secelean, S. Mathew, D. Wardowski, New fixed point results in quasi-metric spaces and applications in Fractals Theory, Advances in Difference Equations 2019 (2019), 1-23.