Cite

[1] M. Alomari and M. Darus, The Hadamard’s inequality for s-convex function, Int. J. Math. Anal. (Ruse), 2 (13-16), (2008), 639-646 Search in Google Scholar

[2] M. Alomari and M. Darus, Hadamard-type inequalities for s-convex functions, Int. Math. Forum, 3 (37-40), (2008), 1965-1975 Search in Google Scholar

[3] G. A. Anastassiou, Univariate Ostrowski inequalities, revisited, Monatsh. Math., 135 (3), (2002), 175-18910.1007/s006050200015 Search in Google Scholar

[4] G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen, Generalized convexity and inequalities, J. Math. Anal. Appl., 335, (2007), 1294-130810.1016/j.jmaa.2007.02.016 Search in Google Scholar

[5] N. S. Barnett, P. Cerone, S. S. Dragomir, M. R. Pinheiro, and A. Sofo, Ostrowski type inequalities for functions whose modulus of the derivatives are convex and applications, Inequality Theory and Applications, Vol. 2, Nova Sci. Publ., Hauppauge, NY, 2003, 19-32; Preprint RGMIA Res. Rep. Coll. 5 (2) (2002), Art. 1 [Online http://rgmia.org/papers/v5n2/Paperwapp2q.pdf] Search in Google Scholar

[6] E. F. Beckenbach, Convex functions, Bull. Amer. Math. Soc., 54, (1948), 439-46010.1090/S0002-9904-1948-08994-7 Search in Google Scholar

[7] M. Bombardelli and S. Varošanec, Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl., 58 (9), (2009), 1869-187710.1016/j.camwa.2009.07.073 Search in Google Scholar

[8] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen R¨aumen. (German), Publ. Inst. Math. (Beograd) (N.S.), 23 (37), (1978), 13-20 Search in Google Scholar

[9] W. W. Breckner and G. Orbán, Continuity properties of rationally s-convex mappings with values in an ordered topological linear space, Universitatea Babeş-Bolyai, Facultatea de Matematica, Cluj-Napoca, 1978 Search in Google Scholar

[10] P. Cerone and S. S. Dragomir, Midpoint-type rules from an inequalities point of view, Handbook of Analytic-Computational Methods in Applied Mathematics, Ed. by G. A. Anastassiou, CRC Press, New York, 135-20010.1201/9780429123610-4 Search in Google Scholar

[11] P. Cerone and S. S. Dragomir, New bounds for the three-point rule involving the Riemann-Stieltjes integrals, Advances in Statistics Combinatorics and Related Areas Ed. by C. Gulati, World Science Publishing, 2002, 53-6210.1142/9789812776372_0006 Search in Google Scholar

[12] P. Cerone and S. S. Dragomir, Some Ostrowski type inequalities for n-time differentiable mappings and applications, Demonstratio Mathematica, 32 (2), (1999), 697-71210.1515/dema-1999-0404 Search in Google Scholar

[13] G. Cristescu, Hadamard type inequalities for convolution of h-convex functions, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity, 8, (2010), 3-11 Search in Google Scholar

[14] S. S. Dragomir, Ostrowski’s inequality for monotonous mappings and applications, J. KSIAM, 3 (1), (1999), 127-135 Search in Google Scholar

[15] S. S. Dragomir, The Ostrowski’s integral inequality for Lipschitzian mappings and applications, Comp. Math. Appl., 38, (1999), 33-3710.1016/S0898-1221(99)00282-5 Search in Google Scholar

[16] S. S. Dragomir, On the Ostrowski’s inequality for Riemann-Stieltjes integral, Korean J. Appl. Math., 7, (2000), 477-48510.1007/BF03012272 Search in Google Scholar

[17] S. S. Dragomir, On the Ostrowski’s inequality for mappings of bounded variation and applications, Math. Ineq. & Appl., 4 (1), (2001), 33-4010.7153/mia-04-05 Search in Google Scholar

[18] S. S. Dragomir, On the Ostrowski inequality for Riemann-Stieltjes integral abf(t)du(t) \int_a^b {f\left( t \right)du\left( t \right)} f (t) du (t)where f is of Hölder type and u is of bounded variation and applications, J. KSIAM, 5 (1), (2001), 35-45 Search in Google Scholar

[19] S. S. Dragomir, Ostrowski type inequalities for isotonic linear functionals, J. Inequal. Pure & Appl. Math., 3 (5), (2002), Art. 68 Search in Google Scholar

[20] S. S. Dragomir, An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure Appl. Math., 3 (2), (2002), Article 31, 8 pp Search in Google Scholar

[21] S. S. Dragomir, An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure Appl. Math., 3 (2), (2002), Article 31 Search in Google Scholar

[22] S. S. Dragomir, An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure Appl. Math., 3 (3), (2002), Article 35 Search in Google Scholar

[23] S. S. Dragomir, An Ostrowski like inequality for convex functions and applications, Revista Math. Complutense, 16 (2), (2003), 373-38210.5209/rev_REMA.2003.v16.n2.16807 Search in Google Scholar

[24] S. S. Dragomir, Operator Inequalities of Ostrowski and Trapezoidal Type, Springer, New York, 201210.1007/978-1-4614-1779-8 Search in Google Scholar

[25] S. S. Dragomir, Inequalities of Hermite-Hadamard type for GA-convex functions, Preprint RGMIA Res. Rep. Coll., 18, (2015)10.4067/S0716-09172015000400002 Search in Google Scholar

[26] S. S. Dragomir, P. Cerone, J. Roumeliotis, and S. Wang, A weighted version of Ostrowski inequality for mappings of Hölder type and applications in numerical analysis, Bull. Math. Soc. Sci. Math. Romanie, 42 (90) (4), (1999), 301-314 Search in Google Scholar

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

[28] S.S. Dragomir and S. Fitzpatrick, The Jensen inequality for s-Breckner convex functions in linear spaces, Demonstratio Math., 33 (1), (2000), 43-4910.1515/dema-2000-0106 Search in Google Scholar

[29] S. S. Dragomir and B. Mond, On Hadamard’s inequality for a class of functions of Godunova and Levin, Indian J. Math., 39 (1), (1997), 1-9 Search in Google Scholar

[30] S. S. Dragomir and C. E. M. Pearce, On Jensen’s inequality for a class of functions of Godunova and Levin, Period. Math. Hungar., 33 (2), (1996), 93-10010.1007/BF02093506 Search in Google Scholar

[31] S. S. Dragomir and C. E. M. Pearce, Quasi-convex functions and Hadamard’s inequality, Bull. Austral. Math. Soc., 57, (1998), 377-38510.1017/S0004972700031786 Search in Google Scholar

[32] S. S. Dragomir, J. Pečarić, and L. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (3), (335-341) Search in Google Scholar

[33] S. S. Dragomir and Th. M. Rassias, Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publisher, 200210.1007/978-94-017-2519-4 Search in Google Scholar

[34] S. S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in L1norm and applications to some special means and to some numerical quadrature rules, Tamkang J. of Math., 28, (1997), 239-24410.5556/j.tkjm.28.1997.4320 Search in Google Scholar

[35] S. S. Dragomir and S. Wang, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and some numerical quadrature rules, Appl. Math. Lett., 11, (1998), 105-10910.1016/S0893-9659(97)00142-0 Search in Google Scholar

[36] S. S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in Lpnorm and applications to some special means and to some numerical quadrature rules, Indian J. of Math., 40 (3), (1998), 245-304 Search in Google Scholar

[37] A. El Farissi, Simple proof and refeinment of Hermite-Hadamard inequality, J. Math. Ineq., 4 (3), (2010), 365-36910.7153/jmi-04-33 Search in Google Scholar

[38] E. K. Godunova and V. I. Levin, Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions. (Russian),Numerical mathematics and mathematical physics (Russian), Moskov. Gos. Ped. Inst., Moscow, 1985, 138-142 Search in Google Scholar

[39] H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math, 48 (1), (1994), 100-11110.1007/BF01837981 Search in Google Scholar

[40] I. Işcan, Some new Hermite-Hadamard type inequalities for geometrically convex functions, Mathematics and Statistics, 1 (2), (2013), 86-9110.13189/ms.2013.010211 Search in Google Scholar

[41] I. Işcan, On some new Hermite-Hadamard type inequalities for s-geometrically convex functions, International Journal of Mathematics and Mathematical Sciences, 2014, Article ID 16390110.1155/2014/163901 Search in Google Scholar

[42] E. Kikianty and S. S. Dragomir, Hermite-Hadamard’s inequality and the p-HH-norm on the Cartesian product of two copies of a normed space, Math. Inequal. Appl., (in press) Search in Google Scholar

[43] U. S. Kirmaci, M. Klaričić Bakula, M. EÖzdemir, and J. Pečarić, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193 (1), (2007), 26-3510.1016/j.amc.2007.03.030 Search in Google Scholar

[44] M. A. Latif, On some inequalities for h-convex functions, Int. J. Math. Anal. (Ruse), 4 (29-32), (2010), 1473-1482 Search in Google Scholar

[45] D. S. Mitrinovićand I. B. Lacković, Hermite and convexity, Aequationes Math., 28, (1985), 229-23210.1007/BF02189414 Search in Google Scholar

[46] D. S. Mitrinović and J. E. Pečarić, Note on a class of functions of Godunova and Levin, C. R. Math. Rep. Acad. Sci. Canada, 12 (1), (1990), 33-36 Search in Google Scholar

[47] F.-C. Mitroi and C. I. Spiridon, A Hermite-Hadamard type inequality for multiplicatively convex functions, Annals of the University of Craiova, Mathematics and Computer Science Series, 38 (1), (2011), 96-99 Search in Google Scholar

[48] P. Montel, Sur les functions convexes et les fonctions sousharmoniques, Journal de Math., 9 (7), (1928), 29-60 Search in Google Scholar

[49] C. P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl., 3 (2), (2000), 155-16710.7153/mia-03-19 Search in Google Scholar

[50] M. A. Noor,K.I.Noor, andM.U.Awan, Some inequalities for geometrically-arithmetically h-convex functions, Creat. Math. Inform., 23 (1), (2014), 91-9810.37193/CMI.2014.01.14 Search in Google Scholar

[51] C. E. M. Pearce and A. M. Rubinov, P-functions, quasi-convex functions, and Hadamard-type inequalities, J. Math. Anal. Appl., 240 (1), (1999), 92-10410.1006/jmaa.1999.6593 Search in Google Scholar

[52] J. E. Pečarić and S. S. Dragomir, On an inequality of Godunova-Levin and some refinements of Jensen integral inequality, Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, 1989, 263-268, Preprint, 89-6, Univ. Babeş-Bolyai, Cluj-Napoca, 1989 Search in Google Scholar

[53] J. Pečarić and S. S. Dragomir, A generalization of Hadamard’s inequality for isotonic linear functionals, Radovi Mat. (Sarajevo), 7, (1991), 103-107 Search in Google Scholar

[54] M. Radulescu, S. Radulescu, and P. Alexandrescu, On the Godunova-Levin-Schur class of functions, Math. Inequal. Appl., 12 (4), (2009), 853-86210.7153/mia-12-69 Search in Google Scholar

[55] M. Z. Sarikaya, A. Saglam, and H. Yildirim, On some Hadamard-type inequalities for h-convex functions, J. Math. Inequal., 2 (3), (2008), 335-34110.7153/jmi-02-30 Search in Google Scholar

[56] E. Set, M. E.Özdemir, and M. Z. Sarıkaya, New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications, Facta Univ. Ser. Math. Inform., 27 (1), (2012), 67-82 Search in Google Scholar

[57] M. Z. Sarikaya, E. Set, and M. E.Özdemir, On some new inequalities of Hadamard type involving h-convex functions, Acta Math. Univ. Comenian. (N.S.), 79 (2), (2010), 265-272 Search in Google Scholar

[58] M. Tunç, Ostrowski-type inequalities via h-convex functions with applications to special means, J. Inequal. Appl., 2013, 2013:32610.1186/1029-242X-2013-326 Search in Google Scholar

[59] M. Tunç, On Hadamard type inequalities for s-geometrically convex functions, Preprint RGMIA Research Report Collection, 15, (2012), article 70 Search in Google Scholar

[60] S. Varošanec, On h-convexity, J. Math. Anal. Appl., 326 (1), (303-311)10.1016/j.jmaa.2006.02.086 Search in Google Scholar

[61] X.-M. Zhang and N.-G. Zheng, Geometrically convex functions and estimation of remainder terms for Taylor expansion of some functions, J. Math. Inequal., 4 (1), (2010), 15-2510.7153/jmi-04-03 Search in Google Scholar

[62] X.-M. Zhang, Y.-M. Chu, and X.-H. Zhang, The Hermite-Hadamard type inequality of GA-convex functions and its application, Journal of Inequalities and Applications, 2010, Article ID 50756010.1155/2010/507560 Search in Google Scholar

eISSN:
1841-3307
Idioma:
Inglés
Calendario de la edición:
Volume Open
Temas de la revista:
Mathematics, General Mathematics