TY  - JOUR
T1  - On Hermite-Hadamard type Inequalities for Proportional Caputo-Hybrid Operator
AU  - Sarıkaya, Mehmet Zeki
PY  - 2023
DA  - April
Y2  - 2023
JF  - Konuralp Journal of Mathematics
JO  - Konuralp J. Math.
PB  - Mehmet Zeki SARIKAYA
WT  - DergiPark
SN  - 2147-625X
SP  - 31
EP  - 39
VL  - 11
IS  - 1
LA  - en
AB  - In this study, we present a new generalization of the Hermite-Hadamard type inequalities for convex functions via proportional Caputo-hybrid operator. Also, we give some new inequalities for proportional Caputo-hybrid operator using a newly developed generalized an identity, which is rigorously proven.
KW  - Convex function
KW  - Caputo fractional derivative
KW  - Riemann-Liouville integral and Hermite-Hadamard inequality
CR  - [1] H. Budak, E. Pehlivan and P. Kosem, On new extensions of Hermite-Hadamard inequalities for generalized fractional integrals, Sahand Communications
in Mathematical Analysis, 18(1), 73-88, (2021).
CR  - [2] D. Baleanu, A. Fernandez and A. Akgul, On a fractional operator combining proportional and classical differintegrals, Mathematics, 2020, 8, 360.
CR  - [3] H. Budak, C. C. Bilis¸ik and M. Z. Sarikaya, On some new extensions of inequalities of Hermite-Hadamard type for generalized fractional integrals,
Sahand Communications in Mathematical Analysis, 19(2), 65-79, (2022).
CR  - [4] S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezodial
formula, Appl. Math. lett., 11(5) (1998), 91-95.
CR  - [5] S. S. Dragomir and C. E. M. Pearce, Selected topics on Hermite–Hadamard inequalities and applications, RGMIA Monographs, Victoria University,
2000.
CR  - [6] M. G¨urb¨uz, A. O. Akdemir and M. A. Dokuyucu, Novel approaches for differentiable convex functions via the proportional Caputo-hybrid operators,
Fractal and Fractional, 6(5), 258, (2022).
CR  - [7] H. Kavurmaci, M. Avci and M.E. O¨ zdemir, New inequalities of Hermite-Hadamard type for convex functions with applications, J. Inequalities Appl.
2011, 2011, 86.
CR  - [8] U.S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comput.
2004, 147, 137–146.
CR  - [9] U. S. Kirmaci, M. K. Bakula, M. E.O¨ zdemir and J. Pecˇaric´, Hadamard-type inequalities for s-convex functions, Applied Mathematics and Computation,
193(1), 26-35, (2007).
CR  - [10] D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers,
Dordrecht, 1994.
CR  - [11] P. O. Mohammed and I. Brevik, A new version of the Hermite–Hadamard inequality for Riemann–Liouville fractional integrals,. Symmetry, 12(4), 610,
(2020).
CR  - [12] S. G. Samko, A. A Kilbas, O. I. Marichev, Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York, 1993.
CR  - [13] H. ¨O˘g¨ulm¨us¸ and M. Z. Sarikaya, Some Hermite–Hadamard type inequalities for h-convex functions and their applications, Iranian Journal of Science
and Technology, Transactions A: Science, 44, 813-819, (2020).
CR  - [14] M.Z. Sarikaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals, Miskolc Mathematical Notes, 17(2),
1049-1059, (2016).
CR  - [15] M.Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math.
Comput. Model. 57, 2403–2407 (2013).
CR  - [16] M.Z. Sarikaya, F. Ertugral, On the generalized Hermite-Hadamard inequalities, Annals of the University of Craiova-Mathematics and Computer Science
Series 47 (2020), no. 1, 193-213.
CR  - [17] M.Z. Sarikaya, H. Budak, Generalized Hermite-Hadamard type integral inequalities for fractional integrals, Filomat 30 (2016), no. 5, 1315–1326.
CR  - [18] M. Z. Sarikaya and N. Aktan, On the generalization of some integral inequalities and their applications, Mathematical and computer Modelling,
54(9-10), 2175-2182, (2011).
CR  - [19] Y. Zhang, J. Wang, On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals, J. Inequal. Appl. 2013 (2013), Art.
number 220.
CR  - [20] J. Wang, X. Li, M. Feckan, Y. Zhou, Hermite–Hadamard-type inequalities for Riemann–Liouville fractional integrals via two kinds of convexity, Appl.
Anal. 92 (2012), no. 11, 2241–2253.
CR  - [21] J. Wang, X. Li, C. Zhu, Refinements of Hermite-Hadamard type inequalities involving fractional integrals, Bull. Belg. Math. Soc. Simon Stevin 20
(2013), 655–666.
CR  - [22] J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means, Journal of Inequalities and
Applications, 2013(1), 1-15, (2013).
UR  - https://dergipark.org.tr/en/pub/konuralpjournalmath/issue//1285660
L1  - https://dergipark.org.tr/en/download/article-file/3094350
ER  -