International Journal of Nonlinear Analysis and Applications
Hermite-Hadamard type fractional integral inequalities for strongly generalized-prequasi-invex function
Document Type : Research Paper
Authors
Department of Basics Sciences, University of Engineering and Technology, Taxila, Pakistan
Abstract
In this research paper we studied strongly generalized-prequasi-invex function. Built on the new definition, $k$-Riemann–Liouville fractional integral inequalities for strongly generalized-prequasi-invex functions are estimated. A bunch of new Hermite–Hadamard type Inequalities in this direction via Katugampola fractional integrals are also derived.
Keywords
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[11] E.R. Nwaeze, S. Kermausuor, and A.M. Tameru, Some new k-riemann–liouville fractional integral inequalities
associated with the strongly η-quasiconvex functions with modulus µ ≥ 0, J. Inequal. Appl. 2018 (2018), no. 1,
1–10.
[12] A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev, and R.H. Romer, Integrals and series, 1988.
[13] J.R. Wang, C. Zhu, and Y. Zhou, New generalized hermite-hadamard type inequalities and applications to special
means, J. Inequal. Appl. 2013 (2013), no. 1, 1–15.
[14] T. Weir and V. Jeyakumar, A class of nonconvex functions and mathematical programming, Bull. Aust. Math.
Soci. 38 (1988), no. 2, 177–189.
[15] T. Weir and B. Mond, Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl. 136 (1988),
no. 1, 29–38.
[16] X.M. Yang, X.Q. Yang, and K.L. Teo, Characterizations and applications of prequasi-invex functions, J. Optim.
Theory Appl. 110 (2001), no. 3, 645–668.
1287–1293.
[2] Wang Haiying and Fu Zufeng, Characterizations and applications of quasi a-preinvex functions, 7th Int. Conf.
Intell. Human-Machine Syst. Cyber., vol. 1, IEEE, 2015, pp. 345–348.
[3] I. I¸scan, Hermite-hadamard’s inequalities for prequasiinvex functions via fractional integrals, Konuralp J. Math.
2 (2012), no. 2, 76–84.
[4] U.N. Katugampola, A new approach to generalized fractional derivatives, arXiv preprint arXiv:1106.0965 (2011).
[5] S. Kermausuor and E.R. Nwaeze, New integral inequalities of hermite–hadamard type via the katugampola fractional integrals for strongly η-quasiconvex functions, J. Anal. 29 (2021), no. 3, 633–647.[6] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and applications of fractional differential equations, vol.
204, elsevier, 2006.
[7] M.A. Latif and S.S. Dragomir, On hermite-hadamard type integral inequalities for n-times differentiable logpreinvex functions, Filomat 29 (2015), no. 7, 1651–1661.
[8] B.B. Mohsen, M.A. Noor, K.I. Noor, and M. Postolache, Strongly convex functions of higher order involving
bifunction, Math. 7 (2019), no. 11, 1028.
[9] M. Muddassar, S.S. Dragomir, and Z. Hussain, Rayna’s fractional integral operations on hermite–hadamard inequalities with η-g-preinvex functions, Adv. Oper. Theory 5 (2020), no. 4, 1390–1405.
[10] M.A. Noor, Hermite-hadamard integral inequalities for log-preinvex functions, J. Math. Anal. Approx. Theory 2
(2007), no. 2, 126–131.
[11] E.R. Nwaeze, S. Kermausuor, and A.M. Tameru, Some new k-riemann–liouville fractional integral inequalities
associated with the strongly η-quasiconvex functions with modulus µ ≥ 0, J. Inequal. Appl. 2018 (2018), no. 1,
1–10.
[12] A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev, and R.H. Romer, Integrals and series, 1988.
[13] J.R. Wang, C. Zhu, and Y. Zhou, New generalized hermite-hadamard type inequalities and applications to special
means, J. Inequal. Appl. 2013 (2013), no. 1, 1–15.
[14] T. Weir and V. Jeyakumar, A class of nonconvex functions and mathematical programming, Bull. Aust. Math.
Soci. 38 (1988), no. 2, 177–189.
[15] T. Weir and B. Mond, Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl. 136 (1988),
no. 1, 29–38.
[16] X.M. Yang, X.Q. Yang, and K.L. Teo, Characterizations and applications of prequasi-invex functions, J. Optim.
Theory Appl. 110 (2001), no. 3, 645–668.
)
Volume 13, Issue 2
July 2022Pages 515-525
- Receive Date: 09 March 2021
- Revise Date: 18 May 2021
- Accept Date: 29 May 2021