Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals

• Published in: Journal of inequalities and applications Vol. 2017; no. 1; pp. 55 - 10
• Main Authors: Agarwal, Praveen, Jleli, Mohamed, Tomar, Muharrem
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 04.03.2017; SpringerOpen
• Subjects: ( k , s ) $(k, s)$ -fractional integral; ( k , s ) $(k, s)$ -Riemann-Liouville fractional integral; Analysis; Applications of Mathematics; generalized k-fractional integral; Hermite-Hadamard inequality; Inequalities; Integrals; Mathematics; Mathematics and Statistics; Texts; generalized; 26A51; Hermite-Hadamard inequality; Riemann-Liouville fractional integral; 26A33; fractional integral; 26D15; [Formula: see text]-Riemann-Liouville fractional integral; [Formula: see text]-fractional integral; generalized k-fractional integral
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-017-1318-y

Some Hermite-Hadamard type inequalities for generalized k -fractional integrals (which are also named ( k , s ) -Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.