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On Hermite-Hadamard type Inequalities for Proportional Caputo-Hybrid Operator

Year 2023, Volume: 11 Issue: 1, 31 - 39, 30.04.2023

Mehmet Zeki Sarıkaya

Abstract

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.

Keywords

Convex function Caputo fractional derivative Riemann-Liouville integral and Hermite-Hadamard inequality

References

  • [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).
  • [2] D. Baleanu, A. Fernandez and A. Akgul, On a fractional operator combining proportional and classical differintegrals, Mathematics, 2020, 8, 360.
  • [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).
  • [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.
  • [5] S. S. Dragomir and C. E. M. Pearce, Selected topics on Hermite–Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000.
  • [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).
  • [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.
  • [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.
  • [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).
  • [10] D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers, Dordrecht, 1994.
  • [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).
  • [12] S. G. Samko, A. A Kilbas, O. I. Marichev, Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York, 1993.
  • [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).
  • [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).
  • [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).
  • [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.
  • [17] M.Z. Sarikaya, H. Budak, Generalized Hermite-Hadamard type integral inequalities for fractional integrals, Filomat 30 (2016), no. 5, 1315–1326.
  • [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).
  • [19] Y. Zhang, J. Wang, On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals, J. Inequal. Appl. 2013 (2013), Art. number 220.
  • [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.
  • [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.
  • [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).

Year 2023, Volume: 11 Issue: 1, 31 - 39, 30.04.2023

Mehmet Zeki Sarıkaya

Abstract

References

  • [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).
  • [2] D. Baleanu, A. Fernandez and A. Akgul, On a fractional operator combining proportional and classical differintegrals, Mathematics, 2020, 8, 360.
  • [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).
  • [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.
  • [5] S. S. Dragomir and C. E. M. Pearce, Selected topics on Hermite–Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000.
  • [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).
  • [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.
  • [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.
  • [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).
  • [10] D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers, Dordrecht, 1994.
  • [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).
  • [12] S. G. Samko, A. A Kilbas, O. I. Marichev, Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York, 1993.
  • [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).
  • [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).
  • [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).
  • [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.
  • [17] M.Z. Sarikaya, H. Budak, Generalized Hermite-Hadamard type integral inequalities for fractional integrals, Filomat 30 (2016), no. 5, 1315–1326.
  • [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).
  • [19] Y. Zhang, J. Wang, On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals, J. Inequal. Appl. 2013 (2013), Art. number 220.
  • [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.
  • [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.
  • [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).
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehmet Zeki Sarıkaya

Publication Date April 30, 2023
Submission Date April 19, 2023
Acceptance Date April 29, 2023
Published in Issue Year 2023 Volume: 11 Issue: 1

Cite

APA Sarıkaya, M. Z. (2023). On Hermite-Hadamard type Inequalities for Proportional Caputo-Hybrid Operator. Konuralp Journal of Mathematics, 11(1), 31-39.
AMA Sarıkaya MZ. On Hermite-Hadamard type Inequalities for Proportional Caputo-Hybrid Operator. Konuralp J. Math. April 2023;11(1):31-39.
Chicago Sarıkaya, Mehmet Zeki. “On Hermite-Hadamard Type Inequalities for Proportional Caputo-Hybrid Operator”. Konuralp Journal of Mathematics 11, no. 1 (April 2023): 31-39.
EndNote Sarıkaya MZ (April 1, 2023) On Hermite-Hadamard type Inequalities for Proportional Caputo-Hybrid Operator. Konuralp Journal of Mathematics 11 1 31–39.
IEEE M. Z. Sarıkaya, “On Hermite-Hadamard type Inequalities for Proportional Caputo-Hybrid Operator”, Konuralp J. Math., vol. 11, no. 1, pp. 31–39, 2023.
ISNAD Sarıkaya, Mehmet Zeki. “On Hermite-Hadamard Type Inequalities for Proportional Caputo-Hybrid Operator”. Konuralp Journal of Mathematics 11/1 (April 2023), 31-39.
JAMA Sarıkaya MZ. On Hermite-Hadamard type Inequalities for Proportional Caputo-Hybrid Operator. Konuralp J. Math. 2023;11:31–39.
MLA Sarıkaya, Mehmet Zeki. “On Hermite-Hadamard Type Inequalities for Proportional Caputo-Hybrid Operator”. Konuralp Journal of Mathematics, vol. 11, no. 1, 2023, pp. 31-39.
Vancouver Sarıkaya MZ. On Hermite-Hadamard type Inequalities for Proportional Caputo-Hybrid Operator. Konuralp J. Math. 2023;11(1):31-9.
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