TY - JOUR T1 - The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators AU - Türkay, Merve Esra AU - Sarıkaya, Mehmet Zeki AU - Yıldırım, Hüseyin PY - 2022 DA - April Y2 - 2022 JF - Konuralp Journal of Mathematics JO - Konuralp J. Math. PB - Mehmet Zeki SARIKAYA WT - DergiPark SN - 2147-625X SP - 79 EP - 86 VL - 10 IS - 1 LA - en AB - In [11], Sarikaya and Ertuğral described a new left-sided and right-sided generalized fractional integrals. The goal of this study obtain the new Hermite-Hadamard-Fejer inequality for the this generalized fractional integrals. New results obtained from the this study are supported from previous works. KW - Hermite-Hadamard inequality KW - Hermite-Hadamard-Fejer inequality KW - Riemann-Liouville fractional integral KW - convex function. CR - [1] H. Budak and Y. Bakis¸, On Fejer type inequalities for products two convex functions. Note Di Matematica, 40(1) (2020), 27-44. CR - [2] H. Budak, On Fej´er type inequalities for convex mappings utilizing fractional integrals of a function with respect to another function. Results in Mathematics, 74(1) (2019), 29. CR - [3] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58. CR - [4] F. Ertu˘gral, M. Z. Sarikaya and H. Budak, On Refinements of Hermite-Hadamard-Fej´er Type Inequalities for Fractional Integral Operators. Applications & Applied Mathematics, 13(1) (2018). CR - [5] L. Fej´er, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian). CR - [6] J. Hadamard, ´ Etude sur les propri´et´es des fonctions enti`eres et en particulier d’une fonction consid´er´ee par Riemann, J. Math. Pures Appl., 58 (1893), 171-215. CR - [7] ˙I.˙Is¸can, Hermite-Hadamard-Fej´er type integral inequalities for convex functions via fractional integrals, Stud. Univ. Babes-Bolyai Math. 60(2015), No. 3, 355–366. CR - [8] M.Z. Sarikaya, On new Hermite Hadamard Fej´er type integral inequalities, Stud. Univ. Babes-Bolyai Math. 57 (3) (2012), 377–386. CR - [9] M.Z. Sarıkaya and H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, Abstract an Applied Analysis, 2012 (2012) 10 pages, Article ID 428983. doi:10.1155/2012/428983 CR - [10] M.Z. Sarıkaya, E. Set, H. Yaldız and N. Basak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57(9) (2013), 2403-2407. CR - [11] M. Z. Sarikaya, F. Ertu˘gral, On the generalized Hermite-Hadamard Inequalities, Annals of the University of Craiova, Mathematics and Computer Science Series Volume 47(1), 2020, Pages 193–213 ISSN: 1223-6934. CR - [12] E. Set, I. Iscan, M.E. Ozdemir and M.Z. Sarıkaya, On New Inequalities of Hermite-Hadamard-Fejer type for convex functions via fractional integrals, Applied Mathematics and Computation, 259 (2015) 875–881. CR - [13] M.Z. Sarikaya and S. Erden, On The Hermite- Hadamard-Fejer Type Integral Inequality for Convex Function, Turkish Journal of Analysis and Number Theory, 2014, Vol. 2, No. 3, 85-89. CR - [14] J. Park, Inequalities of Hermite-Hadamard-Fej´er Type for Convex Functions via Fractional Integrals, International Journal of Mathematical Analysis,Vol. 8, 2014, no. 59, pp. 2927-2937. CR - [15] Prudnikov, A.P., Brychkov Y.A. and Marichev, O.I., Integral and series. In: Elementary Functions, vol. 1. Nauka, Moscow, (1981). CR - [16] M. Z. Sarikaya and H. Budak, On Fejer type inequalities via local fractional integrals. J. Fract. Calc. Appl, 8(1) (2017), 59-77. CR - [17] Wang, J., Zhu C. and Zhou, Y. ”New generalized Hermite-Hadamard type inequalities and applications to special means”, J. Inequal. Appl., 2013(325) (2013), 15 pages. CR - [18] K. L. Tseng, S. R. Hwang, S. S. Dragomir, Fej´er-type inequalities (I), J. Inequal. Appl., 2010 (2010), Art ID: 531976, 7 pages. UR - https://dergipark.org.tr/en/pub/konuralpjournalmath/issue//1022164 L1 - https://dergipark.org.tr/en/download/article-file/2075758 ER -