Generalised Local Fractional Hermite-Hadamard Type Inequalities on Fractal Sets
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 generalised notion of convexity. By defin...
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| Published in: | Pan-American journal of mathematics Vol. 3; p. 16 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Mathyze Publishers
12.07.2024
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| ISSN: | 2832-4293, 2832-4293 |
| Online Access: | Get full text |
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| Summary: | 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 generalised notion of convexity. By defining generalised φh-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 generalised φh-s convex mappings onto fractal sets. Our results are then applied to probability theory. |
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| ISSN: | 2832-4293 2832-4293 |
| DOI: | 10.28919/cpr-pajm/3-16 |