Construction of Fractal Functions Using Kannan Mappings and Smoothness Analysis
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910402849275904 |
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| author | Chandra, Subhash Verma, Saurabh Abbas, Syed |
| author_facet | Chandra, Subhash Verma, Saurabh Abbas, Syed |
| contents | Let T be a self-map on a metric space (X, d). Then T is called the Kannan map if there exists α, 0 < α< 1/2, such that d(T(x), T(y)) <= α[d(x, T(x)) + d(y, T(y))], for all x, y in X.
This paper aims to introduce a new method to construct fractal functions using Kannan mappings. First, we give the rigorous construction of fractal functions with the help of the Kannan iterated function system (IFS). We also show the existence of a Borel probability measure supported on the attractor of the Kannan IFS satisfying the strong separation condition. Moreover, we study the smoothness of the constructed fractal functions. We end the paper with some examples and graphical illustrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03075 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Construction of Fractal Functions Using Kannan Mappings and Smoothness Analysis Chandra, Subhash Verma, Saurabh Abbas, Syed Dynamical Systems 28A80, 47H10, 28A33, 28A78 Let T be a self-map on a metric space (X, d). Then T is called the Kannan map if there exists α, 0 < α< 1/2, such that d(T(x), T(y)) <= α[d(x, T(x)) + d(y, T(y))], for all x, y in X. This paper aims to introduce a new method to construct fractal functions using Kannan mappings. First, we give the rigorous construction of fractal functions with the help of the Kannan iterated function system (IFS). We also show the existence of a Borel probability measure supported on the attractor of the Kannan IFS satisfying the strong separation condition. Moreover, we study the smoothness of the constructed fractal functions. We end the paper with some examples and graphical illustrations. |
| title | Construction of Fractal Functions Using Kannan Mappings and Smoothness Analysis |
| topic | Dynamical Systems 28A80, 47H10, 28A33, 28A78 |
| url | https://arxiv.org/abs/2301.03075 |