The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators
Yıl 2022,
Cilt: 10 Sayı: 1, 79 - 86, 15.04.2022
Merve Esra Türkay
,
Mehmet Zeki Sarıkaya
,
Hüseyin Yıldırım
Öz
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.
Kaynakça
- [1] H. Budak and Y. Bakis¸, On Fejer type inequalities for products two convex functions. Note Di Matematica, 40(1) (2020), 27-44.
- [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.
- [3] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
- [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).
- [5] L. Fej´er, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).
- [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.
- [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.
- [8] M.Z. Sarikaya, On new Hermite Hadamard Fej´er type integral inequalities, Stud. Univ. Babes-Bolyai Math. 57 (3) (2012), 377–386.
- [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
- [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.
- [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.
- [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.
- [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.
- [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.
- [15] Prudnikov, A.P., Brychkov Y.A. and Marichev, O.I., Integral and series. In: Elementary Functions, vol. 1. Nauka, Moscow, (1981).
- [16] M. Z. Sarikaya and H. Budak, On Fejer type inequalities via local fractional integrals. J. Fract. Calc. Appl, 8(1) (2017), 59-77.
- [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.
- [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.
Yıl 2022,
Cilt: 10 Sayı: 1, 79 - 86, 15.04.2022
Merve Esra Türkay
,
Mehmet Zeki Sarıkaya
,
Hüseyin Yıldırım
Kaynakça
- [1] H. Budak and Y. Bakis¸, On Fejer type inequalities for products two convex functions. Note Di Matematica, 40(1) (2020), 27-44.
- [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.
- [3] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
- [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).
- [5] L. Fej´er, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).
- [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.
- [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.
- [8] M.Z. Sarikaya, On new Hermite Hadamard Fej´er type integral inequalities, Stud. Univ. Babes-Bolyai Math. 57 (3) (2012), 377–386.
- [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
- [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.
- [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.
- [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.
- [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.
- [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.
- [15] Prudnikov, A.P., Brychkov Y.A. and Marichev, O.I., Integral and series. In: Elementary Functions, vol. 1. Nauka, Moscow, (1981).
- [16] M. Z. Sarikaya and H. Budak, On Fejer type inequalities via local fractional integrals. J. Fract. Calc. Appl, 8(1) (2017), 59-77.
- [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.
- [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.