Startseite Fractional dual Simpson-type inequalities for differentiable s-convex functions
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Fractional dual Simpson-type inequalities for differentiable s-convex functions

  • Nesrine Kamouche , Sarra Ghomrani EMAIL logo und Badreddine Meftah ORCID logo
Veröffentlicht/Copyright: 30. November 2023
Analysis
Aus der Zeitschrift Analysis Band 44 Heft 2

Abstract

In this paper, a new integral identity is provided. Based on this equality, Simpson-type dual integral inequalities for functions whose first derivatives are s-convex via Riemann–Liouville fractional integrals are established.

MSC 2020: 26D10; 26D15; 26A51

References

[1] M. Alomari, M. Darus and S. S. Dragomir, New inequalities of Simpson’s type for s-convex functions with applications, Res. Rep, Collection 12 (2009), https://vuir.vu.edu.au/id/eprint/17768. Suche in Google Scholar

[2] D. Baleanu, A. Kashuri, P. O. Mohammed and B. Meftah, General Raina fractional integral inequalities on coordinates of convex functions, Adv. Difference Equ. 2021 (2021), Paper No. 82. 10.1186/s13662-021-03241-ySuche in Google Scholar

[3] S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, JIPAM. J. Inequal. Pure Appl. Math. 10 (2009), no. 3, Article ID 86. Suche in Google Scholar

[4] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen, Publ. Inst. Math. (Beograd) (N. S.) 23(37) (1978), 13–20. Suche in Google Scholar

[5] T. Chiheb, B. Boulares, M. Imsatfia, B. Meftah and A. Moumen, On s-convexity of dual Simpson type integral inequalities, Symmetry 15 (2023), no. 3, Paper No. 733. 10.3390/sym15030733Suche in Google Scholar

[6] T. Chiheb, B. Meftah and A. Dih, Dual Simpson type inequalities for functions whose absolute value of the first derivatives are preinvex, Konuralp J. Math. 10 (2022), no. 1, 73–78. Suche in Google Scholar

[7] L. Dedić, M. Matić and J. Pečarić, On dual Euler–Simpson formulae, Bull. Belg. Math. Soc. Simon Stevin 8 (2001), no. 3, 479–504. 10.36045/bbms/1102714571Suche in Google Scholar

[8] S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), no. 5, 91–95. 10.1016/S0893-9659(98)00086-XSuche in Google Scholar

[9] S. S. Dragomir, R. P. Agarwal and P. Cerone, On Simpson’s inequality and applications, J. Inequal. Appl. 5 (2000), no. 6, 533–579. 10.1155/S102558340000031XSuche in Google Scholar

[10] S. Ghomrani, B. Meftah, W. Kaidouchi and M. Benssaad, Fractional Hermite–Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated ( l o g , ( α , m ) ) -preinvex, Afr. Mat. 32 (2021), no. 5–6, 925–940. 10.1007/s13370-021-00870-0Suche in Google Scholar

[11] S. Hamida and B. Meftah, Fractional Bullen type inequalities for differentiable preinvex functions, ROMAI J. 16 (2020), no. 2, 63–74. Suche in Google Scholar

[12] W. Kaidouchi, B. Meftah, M. Benssaad and S. Ghomrani, Fractional Hermite–Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated extended ( s 1 , m 1 ) - ( s 2 , m 2 ) -preinvex, Real Anal. Exchange 44 (2019), no. 2, 305–332. Suche in Google Scholar

[13] N. Kamouche, S. Ghomrani and B. Meftah, Fractional Simpson like type inequalities for differentiable s-convex functions, J. Appl. Math. Stat. Inform. 18 (2022), no. 1, 73–91. 10.2478/jamsi-2022-0006Suche in Google Scholar

[14] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006. Suche in Google Scholar

[15] W. Liu, Ostrowski type fractional integral inequalities for MT-convex functions, Miskolc Math. Notes 16 (2015), no. 1, 249–256. 10.18514/MMN.2015.1131Suche in Google Scholar

[16] B. Meftah, Fractional Ostrowski type inequalities for functions whose first derivatives are φ-preinvex, J. Adv. Math. Stud. 10 (2017), no. 3, 335–347. 10.1155/2016/5292603Suche in Google Scholar

[17] B. Meftah, Fractional Hermite–Hadamard type integral inequalities for functions whose modulus of derivatives are co-ordinated log -preinvex, Punjab Univ. J. Math. (Lahore) 51 (2019), no. 2, 21–37. 10.36753/mathenot.618335Suche in Google Scholar

[18] B. Meftah, M. Benssaad, W. Kaidouchi and S. Ghomrani, Conformable fractional Hermite–Hadamard type inequalities for product of two harmonic s-convex functions, Proc. Amer. Math. Soc. 149 (2021), no. 4, 1495–1506. 10.1090/proc/15396Suche in Google Scholar

[19] B. Meftah and A. Lakhdari, Dual Simpson type inequalities for multiplicatively convex functions, Filomat 37 (2023), no. 22, 7673–7683. 10.1090/proc/16292Suche in Google Scholar

[20] B. Meftah and K. Mekalfa, Some weighted trapezoidal type inequalities via h-preinvexity, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 24(542) (2020), 81–97. 10.21857/9xn31coznySuche in Google Scholar

[21] B. Meftah, M. Merad, N. Ouanas and A. Souahi, Some new Hermite-Hadamard type inequalities for functions whose nth derivatives are convex, Acta Comment. Univ. Tartu. Math. 23 (2019), no. 2, 163–178. 10.12697/ACUTM.2019.23.15Suche in Google Scholar

[22] P. O. Mohammed and T. Abdeljawad, Modification of certain fractional integral inequalities for convex functions, Adv. Difference Equ. 2020 (2020), Paper No. 69. 10.1186/s13662-020-2541-2Suche in Google Scholar

[23] P. O. Mohammed and M. Z. Sarikaya, On generalized fractional integral inequalities for twice differentiable convex functions, J. Comput. Appl. Math. 372 (2020), Article ID 112740. 10.1016/j.cam.2020.112740Suche in Google Scholar

[24] J. Pečarić and A. Vukelić, General dual Euler–Simpson formulae, J. Math. Inequal. 2 (2008), no. 4, 511–526. 10.7153/jmi-02-46Suche in Google Scholar

[25] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Math. Sci. Eng. 187, Academic Press, Boston, 1992. Suche in Google Scholar

[26] W. Saleh, B. Meftah and A. Lakhdari, Quantum dual Simpson type inequalities for q-differentiable convex functions, Int. J. Nonlinear Anal. Appl. 14 (2023), no. 4, 63–76. Suche in Google Scholar

[27] M. Z. Sarikaya and H. Budak, Generalized Hermite–Hadamard type integral inequalities for fractional integrals, Filomat 30 (2016), no. 5, 1315–1326. 10.2298/FIL1605315SSuche in Google Scholar

[28] M. Z. Sarikaya, E. Set, H. Yaldiz and N. Başak, Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model. 57 (2013), no. 9–10, 2403–2407. 10.1016/j.mcm.2011.12.048Suche in Google Scholar

[29] M. Z. Sarikaya and H. Yildirim, On Hermite–Hadamard type inequalities for Riemann–Liouville fractional integrals, Miskolc Math. Notes 17 (2016), no. 2, 1049–1059. 10.18514/MMN.2017.1197Suche in Google Scholar

[30] E. Set, M. E. Özdemir and M. Z. Sarıkaya, New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications, Facta Univ. Ser. Math. Inform. 27 (2012), no. 1, 67–82. Suche in Google Scholar

Received: 2022-05-14
Revised: 2023-08-15
Accepted: 2023-10-10
Published Online: 2023-11-30
Published in Print: 2024-05-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 1.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/anly-2022-1072/html?lang=de
Button zum nach oben scrollen