Abstract
In this note, we get solutions focusing on integral inequalities of Hermite–Hadamard type and unusual attached to it, with \(\eta\)-G-pre invex functions by the way of fractional integral operator selected by Raina R. K.
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References
Antczak, T.: \(G\)-pre-invex functions in mathematical programming. J. Comput. Appl. Math. 217(1), 212–226 (2007)
Antczak, T.: New optimality conditions and duality results of \(G\)-type in differentiable mathematical programming. Nonlinear Anal. 66(7), 1617–1632 (2007)
Agarwal, R.P., Luo, M.J., Raina, R.K.: On Ostrowski Type Inequalities. Fasciculi Mathematici 56(1), 5–37 (2016)
Barani, A., Ghazanfari, A.G.: Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions. Banach J. Math. Anal. 9(2), 9–20 (2015)
Dragomir, S.S., Pecaric, J., Persson, L.E.: Some inequalities of Hadamard type. Soochow J. Math. 21(3), 335–341 (1995)
Dragomir, S.S., Pearce, C.E.M.: Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Vic-toria University (2002)
Gordji, M.E., Delavar, M.R., Dragomir, S.S.: Some inequality related to \(\eta\)-convex function-II. RGMIA Res. Rep. Coll. 18, 1–14 (2015)
Gordji, M.E., Delavar, M.R., Dragomir, S.S.: An inequality related to \(\eta\)-convex functions. Int. J. Nonlinear Anal. Appl. 6(2), 27–33 (2015)
Habib, S., Mubeen, S., Naeem, M.N., Qi, F.: Generalized \(k\) -fractional integral and related inequalites. HAL Arch. (2018)
Iqbal, M., Iqbal, B.M., Nazeer, K.: Generalization of Inequalities Analogous to Hermite-Hadamard Inequality via Fractional Integrals. Bull. Kor. Math. Soc. 52(3), 707–716 (2015)
Khan, M.A., Khurshid, Y., Ali, T.: Hermite-Hadamard In-equality for Fractional Integrals via \(\eta\)-Convex Functions. Acta Math-ematica Universitatis Comenianae 86(1), 153–164 (2017)
Latif, M.A., Dragomir, S.S.: On Hermite-Hadamard type integral inequalities for \(n\)-times differentiable log-preinvex functions. Filomat 29(7), 1651–1661 (2015)
Noor, M.A.: Hermite-Hadamard integral inequalities for logpreinvex functions. J. Math. Anal. Approx. Theory 2, 126–131 (2007)
Noor, M.A., Noor, K.I.: Some characterizations of strongly preinvex functions. J. Math. Anal. Appl. 316, 697–706 (2006)
Ozdemir, M.E., Akdemir, A.O., Set, E.: On \((h; m)\) Convexity and Hadamard Type Inequalities. Transylv. J. Math. Mech. 81, 51–58 (2016)
Pini, R.: Invexity and generalized convexity. Optimization 22, 513–525 (1991)
Raina, R.K.: On generalized Wright’s hypergeometric func-tions and fractional calculus operators. East Asian Math. J. 21(2), 191–203 (2005)
Sarikaya, M.Z., Set, E., Yaldiz, H., Basak, N.: Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Model. 57, 2403–2407 (2017)
Set, E., Celik, B., Akdemir, A.O.: Some new Hermite–Hadamard type inequalities for quasi-convex functions via fractional integral operator. In: American Institute of Physics Conference Proceedings (2017)
Weir, T., Mond, B.: Pre-invex functions in multiple objective optimization. J. Math. Anal. Appl. 136, 29–38 (1988)
Yin, H.P., Wang, J.Y., Qi, F.: Some integral inequalities of hermite-hadamard type for \(s\)-geometrically convex functions. Miskolc Math. Notes (2018)
Yang, X.M., Li, D.: On properties of preinvex functions. J. Math. Anal. Appl. 256, 229–241 (2001)
Yang, X.M., Li, D.: Semistrictly preinvex functions. J. Math. Anal. Appl. 258, 287–308 (2001)
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Communicated by Mario Krnic.
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Muddassar, M., Dragomir, S.S. & Hussain, Z. Rayna’s fractional integral operations on Hermite–Hadamard inequalities with \(\eta\)-G-Preinvex functions. Adv. Oper. Theory 5, 1390–1405 (2020). https://doi.org/10.1007/s43036-020-00045-x
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DOI: https://doi.org/10.1007/s43036-020-00045-x