A comprehensive review of the Hermite-Hadamard inequality pertaining to fractional differential operators
A review on Hermite-Hadamard type inequalities connected with a different classes of convexities and fractional differential operators is presented. In the various classes of convexities it includes, classical convex functions, quasi-convex functions, p-convex functions, strongly-m-convex functions,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University Constantin Brancusi of Targu-Jiu
2023-10-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | https://www.utgjiu.ro/math/sma/v18/p18_15.pdf |
| Summary: | A review on Hermite-Hadamard type inequalities connected with a different classes of convexities and fractional differential operators is presented. In the various classes of convexities it includes, classical convex functions, quasi-convex functions, p-convex functions, strongly-m-convex functions, strongly-(θ,m)-convex functions, (s, m)-convex functions, (θ, h- m)-convex functions, strongly (θ, h- m)-convex functions, (h, m)-convex functions of the second type, m-convex functions, h-convex functions, (h,m)-convex functions, relative-convex functions, exponentially (θ, h- m)-convex functions, harmonically h-convex functions and geometric-arithmetically s-convex functions. In the fractional differential operators it includes, Caputo fractional derivative, k-Caputo fractional derivative and Hilfer fractional derivative. |
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| ISSN: | 1843-7265 1842-6298 |