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Hadamard Inequality for (k − r) Riemann-Liouville Fractional Integral Operator via Convexity |
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PP: 205-215 |
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doi:10.18576/pfda/080201
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Author(s) |
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Ankita Chandola,
Rupakshi Mishra Pandey,
Ritu Agarwal,
Ravi P. Agarwal,
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Abstract |
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| Recently, many researchers have published work on the Hermite-Hadamard inequalities, due to their immense importance in the fields of numerical analysis, statistics, optimization and convexity theory. . In this paper, certain new Hermite-Hadamard type integral inequalities have been established using the (k − r) Riemann-Liouville fractional integral operator. We present various inequalities based on different types of the convex functions such as quasi-convex, l-convex, η-convex in the second sense and (β,l)-convex functions. Also, we derive Hermite-Hadamard type inequalities for the product of two l-convex functions and two (β,l)-convex functions using (k − r) Riemann-Liouville fractional integral operator. The results obtained in our work will be helpful in the further study of the convex functions and in the evaluation of the certain mathematical problems.
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