Regularity properties and integral inequalities related to (k; h₁; h₂)-convexity of functions

[1] F. Bernstein and G. Doetsch, Zur Theorie der konvexen Funktionen, Math. Ann., 76, (1915), 514–52610.1007/BF01458222Search in Google Scholar

[2] W.W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen, Publ. Inst. Math., 23, (1978), 13–20Search in Google Scholar

[3] G. Cristescu, M.A. Noor, and M.U. Awan, Bounds of the second degree cumulative frontier gaps of functions with generalized convexity, Carpath. J. Math., 31, (2015), 173-18010.37193/CJM.2015.02.04Search in Google Scholar

[4] S.S. Dragomir and S. Fitzpatrick, The Hadamard0s inequality for s-convex functions in the second sense, Demonstratio Math., 32, (1999), 687–69610.1515/dema-1999-0403Search in Google Scholar

[5] S.S. Dragomir and N.M. Ionescu, On some inequalities for convex-dominated functions, Anal. Numer. Theor. Approx., 19, (1990), 21–28Search in Google Scholar

[6] S.S. Dragomir, J.E. Pečarić, and L.E. Persson, Some inequalities of Hadamard type, Soochow J. Math. (Taiwan), 21, (1995), 335–341Search in Google Scholar

[7] S.S. Dragomir, C.E.M. Pearce, and J.E. Pečarić, Means, g-convex dominated & Hadamard-type inequalities, Tamsui Oxford Univ. J. Math. Sci., 18, (2002), 161–173Search in Google Scholar

[8] E.K. Godunova and V.I. Levin, Neravenstva dlja funkcii _sirokogo klassa soderzascego vypuklye, monotonnye I nekotorye drugie vidy funkii, Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, (1985), 138–142Search in Google Scholar

[9] J. Hadamard, Étude sur les proprietes des fonctions entieres et en particulier d0une fonction considerée par Riemann, J. Math Pures Appl., 58, (1893), 171–215Search in Google Scholar

[10] A. Házy, Bernstein-Doetsch type results for (k; h)-convex functions, Miskolc Math. Notes, 13, (2012), 325–33610.18514/MMN.2012.538Search in Google Scholar

[11] Ch. Hermite, Sur deux limites d0une intégrale dé_nie, Mathesis, 3, (1883), 82Search in Google Scholar

[12] J.L.W.V. Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta. Math., 30, (1906), 175–19310.1007/BF02418571Search in Google Scholar

[13] H. Kavurmacý, M.E. Özdemir, and M.Z. Sarýkaya, New de_nitions and theorems via diérent kinds of convex dominated functions, RGMIA Research Report Collection (Online), 15, (2012)Search in Google Scholar

[14] B. Micherda and T. Rajba, On some Hermite-Hadamard-Fejér inequalities for (k; h)-convex functions, Math. Ineq. Appl., 12, (2012), 931–94010.7153/mia-15-79Search in Google Scholar

[15] M.A. Noor, K.I. Noor, M.U. Awan, and S. Khan, Hermite-Hadamard inequalities for s-Godunova-Levin preinvex functions, J. Adv. Math. Stud., 7, (2014), 12–1910.2298/FIL1407463NSearch in Google Scholar

[16] W. Orlicz, A note on modular spaces I, Bull. Acad. Polon. Sci. Math. Astronom. Phys., 9, (1961), 157–162Search in Google Scholar

[17] M.E. Özdemir, M. Gürbüz, and H. Kavurmacý, Hermite-Hadamard-type inequalities for (g; 'h)-convex dominated functions, J. Inequal. Appl., 184, (2013)10.1186/1029-242X-2013-184Search in Google Scholar

[18] M.E. Özdemir, M. Tunç, and H. Kavurmacý, Two new diérent kinds of convex dominated functions and inequalities via Hermite-Hadamard type, arXiv:1202.2054v1 [math.CA], ( 9 Feb 2012)Search in Google Scholar

[19] M.Z. Sarikaya, A. Saglam, and H. Yildirim, On some Hadamard-type inequalities for h- convex functions, J. Math. Inequal., 2, (2008), 335–34110.7153/jmi-02-30Search in Google Scholar

[20] D.P. Shi, B.Y. Xi, and F. Qi, Hermite-Hadamard Type Inequalities for (m; h1; h2)- Convex Functions Via Riemann-Liouville Fractional Integrals, Turkish J. Anal. Num- ber Th., 2, (2014), 22–2710.12691/tjant-2-1-6Search in Google Scholar

[21] S. Varošanec, On h-convexity, J. Math. Anal. Appl., 32, (2007), 303–311 10.1016/j.jmaa.2006.02.086Search in Google Scholar