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The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators

Year 2022, Volume: 10 Issue: 1, 79 - 86, 15.04.2022

Merve Esra Türkay Mehmet Zeki Sarıkaya Hüseyin Yıldırım

Abstract

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.

Keywords

Hermite-Hadamard inequality Hermite-Hadamard-Fejer inequality Riemann-Liouville fractional integral convex function.

References

  • [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.

Year 2022, Volume: 10 Issue: 1, 79 - 86, 15.04.2022

Merve Esra Türkay Mehmet Zeki Sarıkaya Hüseyin Yıldırım

Abstract

References

  • [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.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Merve Esra Türkay 0000-0003-4429-2685

Mehmet Zeki Sarıkaya

Hüseyin Yıldırım 0000-0001-8855-9260

Publication Date April 15, 2022
Submission Date November 11, 2021
Acceptance Date March 9, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

APA Türkay, M. E., Sarıkaya, M. Z., & Yıldırım, H. (2022). The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators. Konuralp Journal of Mathematics, 10(1), 79-86.
AMA Türkay ME, Sarıkaya MZ, Yıldırım H. The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators. Konuralp J. Math. April 2022;10(1):79-86.
Chicago Türkay, Merve Esra, Mehmet Zeki Sarıkaya, and Hüseyin Yıldırım. “The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators”. Konuralp Journal of Mathematics 10, no. 1 (April 2022): 79-86.
EndNote Türkay ME, Sarıkaya MZ, Yıldırım H (April 1, 2022) The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators. Konuralp Journal of Mathematics 10 1 79–86.
IEEE M. E. Türkay, M. Z. Sarıkaya, and H. Yıldırım, “The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators”, Konuralp J. Math., vol. 10, no. 1, pp. 79–86, 2022.
ISNAD Türkay, Merve Esra et al. “The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators”. Konuralp Journal of Mathematics 10/1 (April 2022), 79-86.
JAMA Türkay ME, Sarıkaya MZ, Yıldırım H. The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators. Konuralp J. Math. 2022;10:79–86.
MLA Türkay, Merve Esra et al. “The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators”. Konuralp Journal of Mathematics, vol. 10, no. 1, 2022, pp. 79-86.
Vancouver Türkay ME, Sarıkaya MZ, Yıldırım H. The Generalized Hermite-Hadamard-Fejer Type Inequalities for Generalized Fractional Integral Operators. Konuralp J. Math. 2022;10(1):79-86.
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