Jensen’s inequality for (p-q)-convex functions and related results

[1] I. Abbas Baloch, A.A. Mughal, Y.M. Chu, A.U. Haq, and M.D.L. Sen, A variant of Jensen-type inequality and related results for harmonic convex functions, AIMS Math. 5 (2020), 6404-–6418.

[2] M. Adil Khan, J. Khan, and J. Pecaric, Generalization of Jensen’s and Jensen-Steffensen’s inequalities by generalized majorization theorem, J. Math. Inequal. 11 (2017), no. 4, 1049–1074.

[3] G.D. Anderson, M.K. Vamanamurtby, and M. Vuorinen, Generalized convexity and inequalities, J. Math. Anal. Appl. 335 (2007), 1294–1308.

[4] H. Barsam, Some new Hermite-Hadamard type inequalities for convex functions, Wavelets Linear Algebra 7 (2020), no. 2, 11–22.

[5] H. Barsam, A.R. Sattarzadeh, Some results on Hermite-Hadamard inequalities, Mahani Math. Res. Cent. 9 (2020), no. 2, 79–86.

[6] C. Chen, M.S. Sallem, and M.S. Zahoor, Some inequalities of generalized p-convex functions concerning Raina’s fractional integral operators, J. Math. 2021 (2021), Article ID 3089553.

[7] D. Choi, M. Krnic, and J. Pecaric, More accurate classes of Jensen-type inequalities for convex and operator convex functions, Math. Inequal. Appl. 21 (2018), no. 2, 301–321.

[8] S.S. Dragomir, Inequalities of Hermite-Hadamard type for HA-convex functions, Moroccan J. Pure Appl. Anal. 3 (2017), no. 3, 83–101.

[9] S.S. Dragomir, Inequalities of Hermite-Hadamard type for GG-convex functions, Indian J. Math. 60 (2018), no. 1, 1–21.

[10] S.S. Dragomir, Inequalities of Hermite-Hadamard type for HH-convex functions, Acta Comment. Univer. Tartuensis Math. 22 (2018), no. 2, 179–190.

[11] S.S. Dragomir, Weighted integral inequalities for GG-convex functions, J. Appl. Math. Inf. 36 (2018), no. 3, 155–171.

[12] S.S. Dragomir, Inequalities of Hermite-Hadamard type for GH-convex functions, Electron. J. Math. Anal. Appl. 7 (2019), no. 2, 244–255.

[13] S.S. Dragomir, R.P. Agarwal, and N.S. Barnett, Inequalities for Beta and Gamma functions via some classical and new integral inequalities, J. Inequal. Appl. 2 (1999), no. 3.

[14] Z. Eken, S. Kemali, G. Tınaztepe, and G. Adilov, The Hermite-Hadamard inequalities for p-convex functions, Hacettepe J. Math. Statist. 50 (2021), no. 5, 1268–1279.

[15] I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe J. Math. Statist. 43 (2014), no. 6, 935–942.

[16] I. Iscan, Hermite-Hadamard type inequalities for p-convex functions, Int. J. Anal. Appl. 11 (2016), no. 2, 137–145.

[17] I. Iscan, Ostrowski type inequalities for p-convex functions, New Trends Math. Sci. 4 (2016), no. 3, 140–150.

[18] I. Iscan and S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput. 238 (2014), 237–244.

[19] M. Kunt and I. Iscan, Hermite-Hadamard-Fejer type inequalities for p-convex functions, Arab. J. Math. Sci. 23 (2017), 215–230.

[20] M. Kunt and I. Iscan, Hermite-Hadamard-Fejer type inequalities for p-convex functions via fractional integrals, Iran. J. Sci. Technol. Trans. Sci. 42 (2018), 2079–2089.

[21] N. Mehreen and M. Anwar, Hadamard and Fejer type inequalities for p-convex functions via Caputo fractional derivatives, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 1, 253–266.

[22] N. Mehreen and M. Anwar, Hermite-Hadamard type inequalities via exponentially p-convex functions and exponentially s-convex functions in second sense with applications, J. Inequal. Appl. 2019 (2019), 92.

[23] C.P. Niculescu, A multiplicative mean value and its applications, Inequality Theory and Applications, Vol.1, Nova Science Publishers, Huntington, New York, 2001, pp. 243–255.

[24] C.P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2000), 155–167.

[25] C.P. Niculescu, Convexity according to means, Math. Inequal. Appl. 6 (2003), 571–579.

[26] C.P. Niculescu and L.E. Persson, Convex Functions and Their Applications, Springer, Monograph, 2004.

[27] M.E. Ozdemir, E. Set, and M. Alomari, Integral inequalities via several kinds of convexity, Creat. Math. Inf. 20 (2011), no. 1, 62–73.

[28] J. Pecaric and J. Peric, New improvement of the converse Jensen inequality. Math. Inequal. Appl. 21 (2018), no. 1, 217–234.

[29] F. Popovici and C.I. Spiridon, The Jensen inequality for (M, N)-convex functions, Ann. Univer. Craiova Math. Comput. Sci. Ser. 38 (2011), no. 4, 63–66.

[30] W. Rudin, Real and Complex Analysis, McGrow-Hill, New York, 1974.

[31] M. Sababheh, Improved Jensen’s inequality. Math. Inequal. Appl. 20 (2017), no. 2, 389–403.

[32] S. Salas, Y. Erdas, T. Toplu and E. Set, On some generalized fractional integral inequalities for p-convex functions, Fractal Fract. 3 (2019), no. 29, 1–9.

[33] J. Sandor, On refinements of certain inequalities for means, Arch. Math. (Brno) 31 (1995), no. 4, 274–282.

[34] M.Z. Sarikaya and H. Budak, On generalized Hermite-Hadamard inequality for generalized convex function, Int. J. Nonlinear Anal. Appl. 8 (2017), no, 2, 209–222.

[35] S. Sezer, Z. Eken, and G. Tnaztepe, Adilov, p-convex functions and their some properties, Numer. Func. Anal. Opt. 42 (2021), no. 4, 443–459.

[36] M. Vivas-Cortez, A. Kashuri, S.I. Butt, M. Tariq, and J. Nasir, Exponential type p-convex function with some related inequalities and their applications, Appl. Math. Inf. Sci. 15 (2021), no. 3, 253–261.

[37] L.C. Wang, On extensions and refinements of Hermite-Hadamard inequalities for convex functions, Math. Inequal. Appl. 6 (2003), 659–666.

[38] W. Wang and J. Qi, Some new estimates of Hermite-Hadamard inequalities for harmonically convex functions with applications, Int. J. Anal. Appl. 13 (2017), no. 1, 15-21.

[39] G. Zabandan, A new refinement of Hermite-Hadamard for convex functions, J. Ineq. Pure Appl. Math. 10 (2009), Article, ID 45.

[40] G. Zabandan, Note on Stirling’s formula and Wallis inequality of order m, Adv. Inequal. Apple. 2015 (2015), Article ID 4.

[41] G. Zabandan, Jensen’s inequality for HH-convex functions and related results, Adv. inequal. Appl. 2016 (2016) Article 10.

[42] G. Zabandan, New Inequalities of Hermite-Hadamard type for MN-convex functions, Adv. Inequal. Appl. 2016 (2016), 7.

[43] G. Zabandan, Jensen’s inequality for GG-convex functions, Int. J. Nonlinear Anal. Appl. 10 (2019), no. 1, 1–7.

[44] G. Zabandan, An extension and refinement of Hermite-Hadamard inequalities and related results, Int. J. Nonlinear Anal. Appl. 11 (2020), no. 2, 379–390.

[45] G. Zabandan, A. Bodaghi, and A. Kilicman, The Hermite-Hadamard inequality for r-convex function, J. Inequal. Appl. 2012 (2012), Article ID 215.

[46] G. Zabandan and A. Kilicman, A new version of Jensen’s inequality and related results, J. Inequal. Appl. 2012 (2012), 238.

[47] K.S. Zhang and J.P. Wan, p-convex functions and their properties, Pure Appl. Math. 23 (2007), no. 1, 130–133.