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.
Digital Object Identifier (DOI)
Chandola, Ankita; Mishra Pandey, Rupakshi; Agarwal, Ritu; and P. Agarwal, Ravi
"Hadamard Inequality for (k − r) Riemann-Liouville Fractional Integral Operator via Convexity,"
Progress in Fractional Differentiation & Applications: Vol. 8:
2, Article 1.
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss2/1