Review Note on Hermite-Hadamard Type Integral Inequality ViaRiemann-Liouville Fractional Integral Operators

Authors

  • Gul Bahar Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro, Pakistan
  • Muhammad Tariq Department of Mathematics, Balochistan Residential College, Loralai, Balochistan,
  • Asif Ali Shaikh Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro, Pakistan
  • Hijaz Ahmad Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey

DOI:

https://doi.org/10.48165/gjs.2024.1107

Keywords:

Preinvex functions, Hadamard inequality, Ψ-Riemann-Liouville Fractional Integral Oprator

Abstract

 In the context of fractional calculus, the concept of convexity is primarily used to tackle various challenges in both theoretical and applied research. This review paper aims to present Hermite–Hadamard (H-H) inequalities related to different classes of
convex functions via Riemann-Liouville fractional integral operators.

Author Biographies

  • Muhammad Tariq, Department of Mathematics, Balochistan Residential College, Loralai, Balochistan,

    Department of Mathematics, Balochistan Residential College, Loralai, Balochistan, Pakistan

  • Hijaz Ahmad, Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey

     Section of Mathematics, International Telematic University Uninettuno, 

    Corso Vittorio Emanuele II, 39,00186 Roma, Italy 

References

[1] Hanson, M.A. On sufficiency of the Kuhn–Tucker conditions. J. Math. Anal. Appl. 1981, 80, 545–550.

[2] Weir, T.; Mond, B. Preinvex functions in multiple-objective optimization. J. Math. Anal. Appl. 1988, 136, 29–38.

[3] Ben-Isreal, A.; Mond, B. What is invexity? J. Aust. Math. Soc. Ser. B. 1986, 28, 1–9. 7

[4] Barani, A.; Ghazanfari, G.; Dragomir, S. S. Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex. J. Inequal. Appl. 2012, 247.

[5] Du, T.T.; Liao, J.G.; Li, Y. J. Properties and integral inequalities of Hadamard-Simpson type for the generalized (s, m)–preinvex functions. J. Nonlinear Sci. Appl. 2016, 9, 3112– 3126.

[6] Deng, Y.; Kalsoom, H.; Wu, S. Some new Quantum Hermite–Hadamard-type estimates within a class of generalized (s, m)—preinvex functions. Symmetry 2019, 11, 1283.

[7] Farajzadeh, A.; Noor, M.A.; Noor, K.I. Vector nonsmooth variational-like inequalities and optimization problems. Nonlinear Anal. 2009, 71, 3471–3476.

[8] Noor, M.A. Variational–like inequalities. Optimization 1994, 30, 323–330.

[9] Du, T.S.; Liao, J.G.; Chen, L.G.; Awan, M.U. Properties and Riemann–Liouville frac-tional Hermite–Hadamard inequalities for the generalized (α, m)-preinvex functions. J. Inequal. Appl. 2016, 2016, 306.

[10] Mitrinovic, D.S.; Pecaric, J.E.; Fink, A.M. Classical and New Inequalities in Analysis; Kluwer Academic: Dordrecht, The Netherlands, 1993.

[11] Anatoli, K. Theory and applications of fractional differential equations, 204, 2006, else vier.

Downloads

Published

2024-11-12

Issue

Vol. 1 No. 1 (2024): Global Journal of Sciences (Jan-Jun)

Section

Review Article

How to Cite

Review Note on Hermite-Hadamard Type Integral Inequality ViaRiemann-Liouville Fractional Integral Operators. (2024). Global Journal of Sciences, 1(1), 67-72. https://doi.org/10.48165/gjs.2024.1107