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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00718 |
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| _version_ | 1866911744829423616 |
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| author | Olanipekun, Peter Olamide |
| author_facet | Olanipekun, Peter Olamide |
| contents | Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this paper, we establish a generalized notion of convexity. By defining generalised $ϕ_{h-s}$ convex functions, we extend the well known concepts of generalised convex functions, $P$-functions, Breckner $s$-convex functions, $h$-convex functions amongst others. With this definition, we prove Hermite-Hadamard type inequalities for generalized $ϕ_{h-s}$ convex mappings onto fractal sets. Our results are then applied to probability theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00718 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalised Local Fractional Hermite-Hadamard Type Inequalities on Fractal Sets Olanipekun, Peter Olamide Functional Analysis Probability Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this paper, we establish a generalized notion of convexity. By defining generalised $ϕ_{h-s}$ convex functions, we extend the well known concepts of generalised convex functions, $P$-functions, Breckner $s$-convex functions, $h$-convex functions amongst others. With this definition, we prove Hermite-Hadamard type inequalities for generalized $ϕ_{h-s}$ convex mappings onto fractal sets. Our results are then applied to probability theory. |
| title | Generalised Local Fractional Hermite-Hadamard Type Inequalities on Fractal Sets |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2401.00718 |