Inequalities of Jensen type for φ-convex functions

• Autorzy: Dragomir S. S.

Identyfikatory

DOI

0.1515/fascmath-2015-0013

• Języki publikacji: EN

Abstrakty

EN

Some inequalities of Jensen type for φ-convex functions defined on real intervals are given.

Słowa kluczowe

EN

convex functions; integral inequalities; h-convex functions

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2015
• Tom: Nr 55
• Strony: 35--52
• Opis fizyczny: Bibliogr. 53 poz.

Twórcy

autor

Dragomir S. S.

• Mathematics, College of Engineering & Science Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia
• School of Computer Science & Applied Mathematics University of the Witwatersrand Private Bag 3, Johannesburg 2050, South Africa

Bibliografia

• [1] Alomari M., Darus M., The Hadamard’s inequality for s-convex function, Int. J. Math. Anal.(Ruse), 2(13-16)(2008), 639-646.
• [2] Alomari M., Darus M., Hadamard-type inequalities for s-convex functions, Int. Math. Forum, 3(37-40)(2008), 1965-1975.
• [3] Anastassiou G.A., Univariate Ostrowski inequalities, revisited, Monatsh. Math., 135(3)(2002), 175-189.
• [4] Barnett N.S., Cerone P., Dragomir S.S., Pinheiro M.R., Sofo A., Ostrowski type inequalities for functions whose modulus of the derivatives are convex and applications, Inequality Theory and Applications, Vol. 2 (Chinju/Masan, 2001), 19-32, Nova Sci. Publ., Hauppauge, NY, 2003. Preprint: RGMIA Res. Rep. Coll.. 5(2002), No. 2, Art. 1 [Online http://rgmia.org/papers/v5n2/Paperwapp2q.pdf]
• [5] Beckenbach E.F., Convex functions, Bull. Amer. Math. Soc., 54(1948), 439-460.
• [6] Bombardelli M, Varošanec S., Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl., 58(9)(2009), 1869-1877.
• [7] Breckner W.W., Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Raumen. (German), Publ. Inst. Math., (Beograd) (N.S.), 23(37)(1978), 13-20.
• [8] Breckner W.W., Orbán G., Continuity Properties of Rationally s-Convex Mappings with Values in an Ordered Topological Linear Space, Universitatea ”Babeş-Bolyai”, Facultatea de Matematica, Cluj-Napoca, 1978, VIII+92 pp.
• [9] Cerone P., Dragomir S.S., Midpoint-type rules from an inequalities point of view, Ed. G. A. Anastassiou, Handbook of Analytic-Computational Methods in Applied Mathematics, CRC Press, New York, 135-200.
• [10] Cerone P., Dragomir S.S., New bounds for the three-point rule involving the Riemann-Stieltjes integrals, Advances in Statistics Combinatorics and Related Areas, C. Gulati, et al. (Eds.), World Science Publishing, 2002, 53-62.
• [11] Cerone P., Dragomir S.S., Roümeliotis J., Some Ostrowski type inequalities for n-time differentiable mappings and applications, Demonstratio Mathematica, 32(2)(1999), 697-712.
• [12] Cristescu G., Hadamard type inequalities for convolution of h-convex functions, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approxx. Convexity, 8(2010), 3-11.
• [13] Dragomir S.S., Ostrowski’s inequality for monotonous mappings and applications, J. KSIAM, 3(1)(1999), 127-135.
• [14] Dragomir S.S., The Ostrowski’s integral inequality for Lipschitzian mappings and applications, Comp. Math. Appl., 38(1999), 33-37.
• [15] Dragomir S.S., On the Ostrowski’s inequality for Riemann-Stieltjes integral, Korean J. Appl. Math., 7(2000), 477-485.
• [16] Dragomir S.S., On the Ostrowski’s inequality for mappings of bounded variation and applications, Math. Ineq. & Appl., 4(1)(2001), 33-40.
• [17] Dragomir S.S., On the Ostrowski inequality for Riemann-Stieltjes integral ʃ^b_a 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.
• [18] Dragomir S.S., Ostrowski type inequalities for isotonic linear functionals, J. Inequal. Pure & Appl. Math., 3(5)(2002), Art. 68.
• [19] Dragomir S.S., 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.
• [20] Dragomir S.S., 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.
• [21] Dragomir S.S., 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.
• [22] Dragomir S.S., An Ostrowski like inequality for convex functions and applications, Revista Math. Complutense, 16(2)(2003), 373-382.
• [23] Dragomir S.S., Operator Inequalities of Ostrowski and Trapezoidal Type, Springer Briefs in Mathematics, Springer, New York, 2012. x+112 pp. ISBN: 978-1-4614-1778-1.
• [24] Dragomir S.S., Inequalities of Hermite-Hadamard type for h-convex func tions on linear spaces, PreprintRGMIA, Res. Rep. Coll., 16(2013), Art. 72, [Online http://rgmia.org/papers/v16/v16a72.pdf].
• [25] Dragomir S.S., Inequalities of Hermite-Hadamard type for p-convex functions, PrerpintRGMIA Res. Rep. Coll., 16(2013), Art..
• [26] Dragomir S.S., Cerone P., Roumeliotis J., Wang S., 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.
• [27] Dragomir S.S., Fitzpatrick S., The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Math., 32(4)(1999), 687-696.
• [28] Dragomir S.S., Fitzpatrick S., The Jensen inequality for s-Breckner convex functions in linear spaces, Demonstratio Math., 33(1)(2000), 43-49.
• [29] Dragomir S.S., Mond B., On Hadamard’s inequality for a class of functions of Godunova and Levin, Indian J. Math., 39(1)(1997), 1-9.
• [30] Dragomir S.S., Pearce C.E.M., On Jensen’s inequality for a class of functions of Godunova and Levin, Period. Math. Hungar., 33(2)(1996), 93-100.
• [31] Dragomir S.S., Pearce C.E.M., Quasi-convex functions and Hadamard’s inequality, Bull. Austral. Math. Soc., 57(1998), 377-385.
• [32] Dragomir S.S., Pečaric J., Persson L., Some inequalities of Hadamard type, Soochow J. Math., 21(3)(1995), 335-341.
• [33] Dragomir S.S., Rassias (Eds Th.M., Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publisher, 2002.
• [34] Dragomir S.S., Wang S., A new inequality of Ostrowski’s type in L₁-norm and applications to some special means and to some numerical quadrature rules, Tamkang J. of Math., 28(1997), 239-244.
• [35] Dragomir S.S., Wang S., 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), 105-109.
• [36] Dragomir S.S., Wang S., A new inequality of Ostrowski’s type in L_p-norm and applications to some special means and to some numerical quadrature rules, Indian J. of Math., 40(3)(1998), 245-304.
• [37] El Farissi A., Simple proof and refeinment of Hermite-Hadamard inequality, J. Math. Ineq., (3)(2010), 365-369.
• [38] Godunova E.K., Levin V.I., Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions, Numerical Mathematics and Mathematical Physics, (Russian), 138-142, 166, Moskov. Gos. Ped. Inst., Moscow, 1985.
• [39] Hudzik H., Maligranda L., Some remarks on s-convex functions, Aequa-tiones Math., 48(1)(1994), 100-111.
• [40] Kikianty E., Dragomir S.S., Hermite-Hadamard’s inequality and the p-HH -norm on the Cartesian product of two copies of a normed space, Math. Inequal. Appl., 13(1)(2010), 1-32.
• [41] Kirmaci U.S., Klaričić Bakula M., Eözdemir M., Pečarić J., Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193(1)(2007), 26-35.
• [42] Latif M.A., On some inequalities for h-convex functions, Int. J. Math. Anal., (Ruse), 4(29-32)(2010), 1473-1482.
• [43] Mitrinović D.S., Lacković I.B., Hermite and convexity, Aequationes Math., 28(1985), 229-232.
• [44] Mitrinović D.S., Pečarić J.E., Note on a class of functions of Godunova and Levin, C. R. Math. Rep. Acad. Sci. Canada, 12(1)(1990), 33-36.
• [45] Pearce C.E.M., Rubinov A.M., P-functions, quasi-convex functions, and Hadamard-type inequalities, J. Math. Anal Appl., 240(1)(1999), 92-104.
• [46] Pečarić J.E., Dragomir S.S., 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.
• [47] Pečarić J.E., Dragomir S.S., A generalization of Hadamard’s inequality for isotonic linear functionals, Radovi Mat. (Sarajevo), 7(1991), 103-107.
• [48] Radulescu M., Radulescu S., Alexandrescu P., On the Godunova-Levin-Schur class of functions, Math. Inequal. Appl., 12(4)(2009), 853-862.
• [49] Sarikaya M.Z., Saglam A., Yildirim H., On some Hadamard-type inequalities for h-convex functions, J. Math. Inequal., 2(3)(2008), 335-341.
• [50] Set E., Özdemir M.E., Sarikaya M.Z., 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.
• [51] Sarikaya M.Z., E. Set E., Özdemir M.E., , On some new inequalities of Hadamard type involving h-convex functions, Acta Math. Univ. Comenian., (N.S.), 79(2)(2010), 265-272.
• [52] Tunç M., Ostrowski-type inequalities via h-convex functions with applications to special means, J. Inequal. Appl., (2013), 326.
• [53] Varošanec S., On h-convexity, J. Math. Anal. Appl., 326(1)(2007), 303-311.