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Some new inequalities for generalized convex functions pertaining generalized fractional integral operators and their applications


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R.P. Agarwal, M.J. Luo and R.K. Raina, On Ostrowski type inequalities. Fasc. Math. 204 (2016), 5–27. Search in Google Scholar

M. Ahmadmir and R. Ullah, Some inequalities of Ostrowski and Grüss type for triple integrals on time scales. Tamkang J. Math. 42(4) (2011), 415–426.10.5556/j.tkjm.42.2011.685 Search in Google Scholar

M. Alomari, M. Darus, S.S. Dragomir and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s–convex in the second sense. Appl. Math. Lett. 23 (2010), 1071–1076. Search in Google Scholar

S.M. Aslani, M.R. Delavar and S.M. Vaezpour, Inequalities of Fejér type related to generalized convex functions with applications. Int. J. Anal. Appl. 16(1) (2018), 38–49.10.1155/2018/5864091 Search in Google Scholar

F.X. Chen and S.H. Wu, Several complementary inequalities to inequalities of Hermite–Hadamard type for s–convex functions. J. Nonlinear Sci. Appl. 9(2) (2016), 705–716.10.22436/jnsa.009.02.32 Search in Google Scholar

M.R. Delavar and M. De La Sen, Some generalizations of Hermite–Hadamard type inequalities. SpringerPlus 5(1661) (2016).10.1186/s40064-016-3301-3 Search in Google Scholar

S.S. Dragomir, On the Ostrowski’s integral inequality for mappings with bounded variation and applications. Math. Ineq. & Appl. 1(2) (1998). Search in Google Scholar

S.S. Dragomir, The Ostrowski integral inequality for Lipschitzian mappings and applications. Comput. Math. Appl. 38 (1999), 33–37. Search in Google Scholar

S.S. Dragomir, Ostrowski-type inequalities for Lebesgue integral: A survey of recent results. Aust. J. Math. Anal. Appl. 14(1) (2017), 1–287. Search in Google Scholar

S.S. Dragomir, Further Ostrowski and trapezoid type inequalities for the generalized Riemann–Liouville fractional integrals of functions with bounded variation. RGMIA Res. Rep. Coll. 20 (2017), Art. 84. Search in Google Scholar

S.S. Dragomir, Ostrowski and trapezoid type inequalities for the generalized k-g–fractional integrals of functions with bounded variation. RGMIA Res. Rep. Coll. 20 (2017), Art. 111. Search in Google Scholar

S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and trapezoidal formula. Appl. Math. Lett. 11(5) (1998), 91–95.10.1016/S0893-9659(98)00086-X Search in Google Scholar

S.S. Dragomir and S. Wang, An inequality of Ostrowski–Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules. Comput. Math. Appl. 13(11) (1997), 15–20.10.1016/S0898-1221(97)00084-9 Search in Google Scholar

S.S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in L1–norm and applications to some special means and to some numerical quadrature rules. Tamkang J. Math. 28 (1997), 239–244. Search in Google Scholar

T.S. Du, M.U. Awan, A. Kashuri and S. Zhao, Some k–fractional extensions of the trapezium inequalities through generalized relative semi–(m,h)–preinvexity. Appl. Anal. (2019). Search in Google Scholar

G. Farid, Existence of an integral operator and its consequences in fractional calculus. Submitted. Search in Google Scholar

G. Farid, Some new Ostrowski type inequalities via fractional integrals. Int. J. Anal. Appl. 14(1) (2017), 64–68.10.30538/oms2017.0010 Search in Google Scholar

J. Hristov, Response functions in linear viscoelastic constitutive equations and related fractional operators. Math. Model. Nat. Phenom. 14(3) (2019), 1–34.10.1051/mmnp/2018067 Search in Google Scholar

M. Jleli and B. Samet, On Hermite–Hadamard type inequalities via fractional integral of a function with respect to another function. J. Nonlinear Sci. Appl. 9 (2016), 1252–1260. Search in Google Scholar

A. Kashuri and R. Liko, Some new Hermite–Hadamard type inequalities and their applications. Stud. Sci. Math. Hung. 56(1) (2019), 103–142.10.1556/012.2019.56.1.1418 Search in Google Scholar

U.N. Katugampola, New approach to a generalized fractional integral. Appl. Math. Comput. 218(3) (2011), 860–865.10.1016/j.amc.2011.03.062 Search in Google Scholar

M.A. Khan, Y.M. Chu, A. Kashuri, R. Liko and G. Ali, Conformable fractional integrals versions of Hermite–Hadamard inequalities and their generalizations. J. Funct. Spaces (2018), Article ID 6928130, pp. 9.10.1155/2018/6928130 Search in Google Scholar

A.A. Kilbas, O.I. Marichev and S.G. Samko, Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach, Switzerland, (1993). Search in Google Scholar

A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier Science B.V., Amsterdam, (2006). Search in Google Scholar

R. Khalil, M.A. Horani, A. Yousef and M. Sababheh, A new de finition of fractional derivatives. J. Comput. Appli. Math. 264 (2014), 65–70. Search in Google Scholar

M. Kirane and B.T. Torebek, Hermite–Hadamard, Hermite–Hadamard–Fejér, Dragomir–Agarwal and Pachpatti type inequalities for convex functions via fractional integrals. arXive:1701.00092. Search in Google Scholar

W.J. Liu, Some Simpson type inequalities for h–convex and (a,m)–convex functions. J. Comput. Anal. Appl. 16(5) (2014), 1005–1012. Search in Google Scholar

W., Liu, W. Wen and J. Park, Hermite–Hadamard type inequalities for MT –convex functions via classical integrals and fractional integrals. J. Nonlinear Sci. Appl. 9 (2016), 766–777. Search in Google Scholar

W. Liu, W. Wen and J. Park, Ostrowski type fractional integral inequalities for MT –convex functions. Miskolc Math. Notes 16(1) (2015), 249–256.10.18514/MMN.2015.1131 Search in Google Scholar

Z. Liu, Some Ostrowski–Grüss type inequalities and applications. Comput. Math. Appl. 53 (2007), 73–79. Search in Google Scholar

Z. Liu, Some companions of an Ostrowski type inequality and applications. J. Inequal. in Pure and Appl. Math. 10(2) (2009), Art. 52, pp. 12. Search in Google Scholar

M. Matloka, Ostrowski type inequalities for functions whose derivatives are h–convex via fractional integrals. Journal of Scienti fic Research and Reports 3(12) (2014), 1633–1641.10.9734/JSRR/2014/10072 Search in Google Scholar

M.V. Mihai, Some Hermite–Hadamard type inequalities via Riemann–Liouville fractional calculus. Tamkang J. Math. 44(4) (2013), 411–416.10.5556/j.tkjm.44.2013.1218 Search in Google Scholar

S. Mubeen and G.M. Habibullah, k–Fractional integrals and applications. Int. J. Contemp. Math. Sci. 7 (2012), 89–94. Search in Google Scholar

M.A. Noor, Some new classes of nonconvex functions. Nonlinear Funct. Anal. Appl. 11 (2006), 165–171. Search in Google Scholar

M.A. Noor, Some properties of nonconvex functions. Nonlinear Funct. Anal. Appl. 23(3) (2018), 575–583. Search in Google Scholar

O. Omotoyinbo and A. Mogbodemu, Some new Hermite–Hadamard integral inequalities for convex functions. Int. J. Sci. Innovation Tech. 1(1) (2014), 1–12.10.1155/2014/796132 Search in Google Scholar

M.E.Özdemir, S.S. Dragomir and C. Yildiz, The Hadamard’s inequality for convex function via fractional integrals. Acta Math. Sci., Ser. B, Engl. Ed. 33(5) (2013), 153–164.10.1016/S0252-9602(13)60081-8 Search in Google Scholar

M.E.Özdemir, H. Kavurmac and E. Set, Ostrowski’s type inequalities for (a,m)–convex functions. Kyungpook Math. J. 50 (2010), 371–378.10.5666/KMJ.2010.50.3.371 Search in Google Scholar

B.G. Pachpatte, On an inequality of Ostrowski type in three independent variables. J. Math. Anal. Appl. 249 (2000), 583–591. Search in Google Scholar

B.G. Pachpatte, On a new Ostrowski type inequality in two independent variables. Tamkang J. Math. 32(1) (2001), 45–49.10.5556/j.tkjm.32.2001.367 Search in Google Scholar

F. Qi and B.Y. Xi, Some integral inequalities of Simpson type for GAe–convex functions. Georgian Math. J. 20(5) (2013), 775–788.10.1515/gmj-2013-0043 Search in Google Scholar

A. Ra fiq, N. A. Mir and F. Ahmad, WeightedČebyšev–Ostrowski type inequalities. Applied Math. Mechanics (English Ed.) 28(7) (2007), 901–906.10.1007/s10483-007-0707-z Search in Google Scholar

M.Z. Sarikaya, On the Ostrowski type integral inequality. Acta Math. Univ. Comenianae 79(1) (2010), 129–134. Search in Google Scholar

M.Z. Sarikaya and F. Ertuğral, On the generalized Hermite–Hadamard inequalities. https://www.researchgate.net/publication/321760443. Search in Google Scholar

M.Z. Sarikaya and H. Yildirim, On generalization of the Riesz potential. Indian Jour. of Math. and Mathematical Sci. 3(2), (2007), 231–235. Search in Google Scholar

M.A. Noor, M.U. Awan and A. Gözpinar, Generalized Hermite–Hadamard type inequalities involving fractional integral operators. J. Inequal. Appl. 169 (2017), 1–10. Search in Google Scholar

R.K. Raina, On generalized Wright’s hypergeometric functions and fractional calculus operators. EAMJ, East Asian Math. J. 21(2) (2005), 191–203. Search in Google Scholar

M. Tomar, P. Agarwal, M. Jleli and B. Samet, Certain Ostrowski type inequalities for generalized s–convex functions. J. Nonlinear Sci. Appl. 10 (2017), 5947–5957. Search in Google Scholar

M. Tunç, Ostrowski type inequalities for functions whose derivatives are MT –convex. J. Comput. Anal. Appl. 17(4) (2014), 691–696. Search in Google Scholar

N. Ujević, Sharp inequalities of Simpson type and Ostrowski type. Comput. Math. Appl. 48 (2004), 145–151. Search in Google Scholar

H. Wang, T.S. Du and Y. Zhang, k–fractional integral trapezium-like inequalities through (h,m)–convex and (a,m)–convex mappings. J. Inequal. Appl. 2017(311) (2017), pp. 20. Search in Google Scholar

B.Y. Xi and F. Qi, Some integral inequalities of Hermite–Hadamard type for convex functions with applications to means. J. Funct. Spaces Appl. 2012 (2012), Article ID 980438, pp. 14. Search in Google Scholar

Ç. Yildiz, M.E.Özdemir and M.Z. Sarikaya, New generalizations of Ostrowski-like type inequalities for fractional integrals. Kyungpook Math. J. 56 (2016), 161–172. Search in Google Scholar

X.M. Zhang, Y.M. Chu and X.H. Zhang, The Hermite–Hadamard type inequality of GA–convex functions and its applications. J. Inequal. Appl. (2010), Article ID 507560, pp. 11. Search in Google Scholar

Y. Zhang, T.S. Du, H. Wang, Y.J. Shen and A. Kashuri, Extensions of different type parameterized inequalities for generalized (m,h)–preinvex mappings via k–fractional integrals. J. Inequal. Appl. 2018 (49) (2018), pp. 30. Search in Google Scholar

L. Zhongxue, On sharp inequalities of Simpson type and Ostrowski type in two independent variables. Comput. Math. Appl. 56 (2008), 2043–2047. Search in Google Scholar

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