New generalized Hermite-Hadamard inequality and related integral inequalities involving Katugampola type fractional integrals
In this paper, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal se...
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Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
MDPI
2020
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Online Access: | http://psasir.upm.edu.my/id/eprint/38275/1/38275.pdf http://psasir.upm.edu.my/id/eprint/38275/ https://www.mdpi.com/2073-8994/12/4/568 |
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Summary: | In this paper, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. This fractional integral generalizes Riemann-Liouville and Hadamard’s integral, which possess a symmetric property. We derive trapezoid and mid-point type inequalities connected to this generalized Hermite-Hadamard inequality. |
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