Viswa - Publications

Research Publications

International Journals

1. R. Medhi, N. Secelean, P. Viswanathan, Exploring Iterative Dynamics, Invariant Measures, and Ergodicity in F-Contractive Iterated Function Systems, Qualitative Theory of Dynamical Systems, 24, 185, (2025), 24 pages.
2. R. Medhi, P. Viswanathan, A Note on the Banach Limit-Based Proof of Elton's Ergodic Theorem for Iterated Function Systems, Topology and Its Applications, 373, (2025), 109519.
3. P. Viswanathan, Casazza-Christensen-Eijndhoven perturbation result in quasi-Banach spaces: application to fractal basic sequences, Complex Analysis and Operator Theory, 19(51), (2025).
4. R. Medhi, P. Viswanathan, The point-fibred property of an iterated function system with local radial contractions and its consequences, Journal of Fixed Point Theory and Applications, (2025), 27:20.
5. P. Viswanathan, An approximation theoretic revamping of fractal interpolation surfaces on triangular domains, Fractional Calculus and Applied Analysis, 27, (2024), 2419-2455.
6. K. K. Pandey, N. A. Secelean, P. Viswanathan, On bivariate fractal interpolation for countable data and associated nonlinear fractal operator, Demonstratio Mathematica, 57, (2024), 20240014.
7. K. K. Pandey, P. Viswanathan, Some elementary properties of Bernstein-Kantorovich operators on mixed norm Lebesgue spaces and their implications in fractal approximation, Nonlinear Analysis - Theory, Method and Applications, 239, (2024) 113416.
8. R. Medhi, P. Viswanathan, The Hutchinson-Barnsley theory for iterated function system with bounded cyclic contractions, Chaos, Solitons and Fractals, 174, (2023) 113796.
9. M. Barnsley, P. Viswanathan, Histopolating fractal functions, Journal of Computational and Applied Mathematics, 425, (2023) 115073.
10. R. Medhi, P. Viswanathan, On the code space and Hutchinson measure for countable iterated function system consisting of cyclic phi-contractions, Chaos, Solitons and Fractals, 167, (2023) 113011.
11. K. K. Pandey, P. Viswanathan, Multivariate fractal interpolation functions: Some approximation aspects and associated fractal interpolation operator, Electronic Transaction on Numerical Analysis, 55, (2022), 627-651.
12. P. Viswanathan, A revisit to smoothness preserving fractal perturbation of a bivariate function: self-referential counterpart to bicubic splines, Chaos, Solitons and Fractals, 157, (2022), 8 pages.
13. K. K. Pandey, P. Viswanathan, In reference to a self-referential approach towards smooth multivariate approximation, Numerical Algorithms, 91, (2022), 251-281.
14. M. A. Navascues, P. Viswanathan, A revisit to stability of Schauder bases: fractalizing multivariate Faber-Schauder system, Fractals, 30, 2 (2022), 12 pages.
15. M. A. Navascues, P. Viswanathan, Bivariate nonlinear fractal approximation in Lebesgue spaces, Jaen Journal on Approximation, 12, (2021), 41-68.
16. P. Viswanathan, A brief exposition of the space of relatively bounded nonlinear operators, Real Analysis Exchange, 47(1), (2021), 121-134.
17. K. K. Pandey, P. Viswanathan, Multivariate fractal functions in some complete function spaces and fractional integral of continuous fractal functions, Fractal and Fractional (invited contribution to Special Issue on Fractal Functions and Applications), 5(4), 185 (2021), 19 pages.
18. P. Viswanathan, A fractal version of a bivariate Hermite polynomial interpolation, Mediterranean Journal of Mathematics, 18, 225 (2021), 15 pages.
19. M. A. Navascues, S. Verma, P. Viswanathan, Concerning the vector-valued fractal interpolation functions on the Sierpinski gasket, Mediterranean Journal of Mathematics, 18, 202 (2021), 26 pages.
20. S. Verma, P. Viswanathan, Katugampola fractional integral and fractal dimension of bivariate functions, Results in Mathematics, 76, 65 (2021), 23 pages.
21. M. A. Navascues, P. Viswanathan, R. Mohapatra, Convolved fractal bases and frames, Advances in Operator Theory, 6, 42 (2021).
22. K. K. Pandey, P. Viswanathan, Countable zipper fractal interpolation and some elementary aspects of the associated nonlinear zipper fractal operator, Aequationes Mathematicae, 95, (2021), 175-200.
23. S. Verma, P. Viswanathan, Parameter identification for a class of bivariate fractal interpolation functions and constrained approximation, Numerical Functional Analysis and Optimization, 41(9), (2020), 1109-1148.
24. S. Verma, P. Viswanathan, A fractalization of rational trigonometric functions, Mediterranean Journal of Mathematics, 17(3), (2020), 23 pp.
25. S. Verma, P. Viswanathan, Fractal Operator Associated with Bivariate Fractal Interpolation Functions on Rectangular Grids, Results in Mathematics, 75(1), (2020), 26 pp.
26. S. Verma, P. Viswanathan, Bivariate functions of bounded variation: fractal dimension and fractional integral, Indagationes Mathematicae, 31(2), (2020), 294-309.
27. P. Viswanathan, Fractal approximation of a function from a countable sample set and associated fractal operator, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Series-A, 114 (32), (2020), 20 pp.
28. A. K. B. Chand, N. Vijender, P. Viswanathan, A. V. Tetenov, Affine zipper fractal interpolation functions, BIT Numerical Mathematics, 60 (2), (2020), 319-344.
29. K. M. Reddy, A. K. B. Chand, P. Viswanathan, Data visualization by rational fractal function based on function values, The Journal of Analysis, 28(1), (2020), 261-277.
30. M. A. Navascues, P. Viswanathan, Perturbation of linear operators on Banach spaces: some applications to Schauder bases and frames, Aequationes Mathematicae, 94 (1), (2019), 13-36.
31. D. Levin, N. Dyn, P. Viswanathan, Non-stationary versions of fixed-point theory, with applications to fractals and subdivision, Journal of Fixed Point Theory and Applications, 21 (1), (2019), 25 pp.
32. M. A. Navascues, P. Viswanathan, Bases of Banach and Hilbert spaces transformed by linear operators, Complex Analysis and Operator Theory, 13, (2019), 2277–2301.
33. S. Verma, P. Viswanathan, A Revisit to α-fractal function and box dimension of its graph, Fractals, 27, 1950090, (2019), 15 pp.
34. M. A. Navascues, P. Viswanathan, Energy minimizing associate fractal functions, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Series-A, 113, (2019), 1025–1039.
35. S. Verma, P. Viswanathan, A note on Katugampola fractional calculus and fractal dimensions, Applied Mathematics and Computations, 339, (2018), 220–230.
36. A. K. B. Chand, P. Viswanathan, N. Vijender, Bicubic partially blended rational fractal surface for a constrained interpolation problem, Computational and Applied Mathematics, 37(1), (2018), 785–805.
37. P. Viswanathan, A. K. B. Chand, K. R. Tyada, Lacunary interpolation by fractal splines with variable scaling parameters, Numerical Mathematics Theory Methods and Applications, 10(1), (2017), 65–83.
38. P. Viswanathan, M. A. Navascues, A fractal operator on some standard spaces of functions, Proceedings of the Edinburgh Mathematical Society, 60(3), (2017), 771–786.
39. A. K. B. Chand, M. A. Navascues, P. Viswanathan, S. K. Katiyar, Fractal trigonometric polynomials for restricted range approximation, Fractals, 24(2), (2016), 1–11.
40. M. F. Barnsley, B. Harding, A. Vince, P. Viswanathan, Approximation of rough functions, Journal of Approximation Theory, 209, (2016), 23–43.
41. P. Viswanathan, M. A. Navascues, A. K. B. Chand, Fractal polynomials and maps in approximation of continuous functions, Numerical Functional Analysis and Optimization, 37(1), (2016), 106–127.
42. P. Viswanathan, M. A. Navascues, A. K. B. Chand, Associate fractal functions in Lp-spaces and in one-sided uniform approximation, Journal of Mathematical Analysis and Applications, 433(2), (2016), 862–876.
43. P. Viswanathan, M. A. Navascues, Fractal functions with function scaling factors as solutions of (0, 4) lacunary interpolation problem, Chaos, Solitons and Fractals, 81, (2015), 98–102.
44. A. K. B. Chand, P. Viswanathan, K. M. Reddy, Towards a more general type of univariate constrained interpolation with fractal splines, Fractals, 23(4), (2015), 1–12.
45. A. K. B. Chand, P. Viswanathan, N. Vijender, Bivariate shape preserving interpolation: A fractal-classical hybrid approach, Chaos, Solitons and Fractals, 81, (2015), 330–344.
46. P. Viswanathan, M. A. Navascues, A. K. B. Chand, A rational iterated function system for resolution of univariate constrained interpolation, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Series-A,109(2), (2015), 483–509.
47. P. Viswanathan, A. K. B. Chand, A C1-rational cubic fractal interpolation function: convergence and associated parameter identification problem, Acta Applicandae Mathematicae, 136(1), (2015), 19–41.
48. P. Viswanathan, A. K. B. Chand, On cubic Hermite coalescence hidden variable fractal interpolation functions, Applied Mathematics-A Journal of Chinese Universities, 30(1), (2015), 55–76.
49. M. A. Navascues, P. Viswanathan, A. K. B. Chand, M. V. Sebastian, S. K. Katiyar, Fractal bases for Banach spaces of smooth functions, Bulletin of the Australian Mathematical Society, 92(3), (2015), 405–419.
50. P. Viswanathan, A. K. B. Chand, Monotone-comonotone approximation using fractal cubic splines and polynomials, Electronic Transaction on Numerical Analysis, 44, (2015), 639–659.
51. A. K. B. Chand, S. K. Katiyar, P. Viswanathan, Approximation using hidden variable fractal interpolation functions, Journal of Fractal Geometry, 2, (2015), 81–114.
52. P. Viswanathan, A. K. B. Chand, A fractal procedure for monotonicity preserving interpolation, Applied Mathematics and Computation, 247, (2014), 190–204.
53. P. Viswanathan, A. K. B. Chand, Fractal rational functions and their approximation properties, Journal of Approximation Theory, 185, (2014), 31–50.
54. P. Viswanathan, A. K. B. Chand, α-fractal constrained fractal interpolation, Electronic Transaction on Numerical Analysis, 41, (2014), 420-442.
55. M. A. Navascues, A. K. B. Chand, P. Viswanathan, M. V. Sebastian, Fractal interpolation functions: A short survey, Applied Mathematics, 5(12), (2014), 1834-1841.
56. P. Viswanathan, A. K. B. Chand, M. A. Navascues, Fractal perturbation preserving fundamental shapes: Bounds on the scale factors, Journal of Mathematical Analysis and Applications, 419(2), (2014), 804-817.
57. P. Viswanathan, A. K. B. Chand, R. P. Agarwal, Preserving convexity through rational cubic spline fractal interpolation function, Journal of Computational and Applied Mathematics, 263, (2014), 262-276.
58. A. K. B. Chand, P. Viswanathan, A constructive approach to cubic Hermite fractal interpolation function and its constrained aspects, BIT Numerical Mathematics, 53, (2013), 841-865.

International Conference Proceedings and Book Chapters

A. K. B. Chand, P. Viswanathan, Cubic Hermite and Cubic Spline Fractal Interpolation Functions, American Institute of Physics Conference Proceeding, 1479 (2012), pp. 1467–1470.
P. Viswanathan, A. K. B. Chand, A New Class of Rational Cubic Fractal Splines for Univariate Interpolation, International Conference in Mathematics and Computing-2013, Springer Proceedings in Mathematics & Statistics Vol. 91, (Eds) R. N. Mohapatra, Debasis Giri, P.K. Saxena, P.D. Srivastava, pp. 103-120.
P. Viswanathan, A. K. B. Chand, On Fractal Rational Functions, Fractals,Wavelets, and their Applications: International Conference and Workshop on Fractals & Wavelets-2013. Springer Proceedings in Mathematics & Statistics Vol. 92, (Eds) C. Bandt, M. Barnsley, R. Devaney, K.J.Falconer, V. Kannan, V. Kumar, pp. 369-382.
A. K. B. Chand, P. Viswanathan, M.A. Navascués, A New Class of Rational Quadratic Fractal Functions with Positive Shape Preservation, Fractals, Wavelets, and their Applications: International Conference and Workshop on Fractals & Wavelets-2013. Springer Proceedings in Mathematics & Statistics Vol. 92, (Eds) C. Bandt, M. Barnsley, R. Devaney, K.J.Falconer, V. Kannan, V. Kumar, pp. 283-301.
P. Viswanathan, A. K. B. Chand, A Rational Cubic Fractal Spline Model for a Positive Data, Proceedings of the International Conference On Mathematics-A Global Scenario, ISBN 978-81-925376-0-8, (2012), pp. 141–147.
A. K. B. Chand, P. Viswanathan, K.M. Reddy, A Novel Approach to Surface Interpolation Fractal Surface: Marriage of Coons Technique and Univariate Fractal Functions, Mathematical Analysis and Applications, Roorkey, India, Springer Proceedings in Mathematics & Statistics Vol.143, (Eds) P. N. Agrawal, R. N. Mohapatra, Uaday Singh, H. M. Srivastava, pp. 577–592.
M. A. Navascués, P. Viswanathan, S. K. Katiyar, A. K. B. Chand, Smooth Fractal Interpolation with Function Scaling Factors, Mathematical and Computational Sciences, (Eds) Santhosh George, Jidesh P., Johny Jose, Narosa Publishing House, ISBN 978-81-8487-456-3, pp. 72–79.

International Conference Presentations

P. Viswanathan, A. K. B. Chand, A New Approach to Positivity Preserving Interpolation Using Smooth α-Fractal Functions, Fractal Geometry and Stochastic V, Tabarz, Germany.
P. Viswanathan, A. K. B. Chand, M. A. Navascués, Uniform Restricted Range Approximation With Self-referential Functions, The 10-th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, Spain.
P. Viswanathan, A. K. B. Chand, Constrained Approximation with Fractal Functions and SAIN Property of Fractal Polynomials, New Directions in Fractal Geometry, Canberra, Australia.

Referee's report: This paper contains much that is new and much that is true. Unfortunately, that which is true is not new and that which is new is not true. In H.Eves Return to Mathematical Circles, Boston: Prindle, Weber, and Schmidt, 1988.

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