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Inequalities of Čebyšev Type for Lipschitzian Functions in Banach Algebras


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1] G. A. Anastassiou, Güss type inequalities for the Stieltjes integral, Nonlinear Funct. Anal. Appl., 12 (4), (2007), 583-593Search in Google Scholar

[2] G. A. Anastassiou, Chebyshev-Güss type and comparison of integral means inequalities for the Stieltjes integral, Panamer. Math. J., 17 (3), (2007), 91-109Search in Google Scholar

[3] G. A. Anastassiou, Chebyshev-Güss type inequalities via Euler type and Fink identities, Math. Comput. Modelling, 45 (9-10), (2007), 1189-120010.1016/j.mcm.2006.09.016Search in Google Scholar

[4] M. Biernacki, Sur une inégalité entre les intégrales due à Tchebyscheff, Ann. Univ. Mariae Curie-Sklodowska, A5, (1951), 23-29Search in Google Scholar

[5] K. Boukerrioua and A. Guezane-Lakoud, On generalization of Čebyšev type inequalities, J. Inequal. Pure Appl. Math., 8 (2, Article 55), (2007), 4 pp.Search in Google Scholar

[6] P. L. Čebyšev, O približennyh vyraženijah odnih integralov čerez drugie, Soobščenija i protokoly zasedaniĭ Matemmatičeskogo občestva pri Imperatorskom Har’kovskom Universitete, 2(93-98)Search in Google Scholar

[7] P.L. Čebyšev, Ob odnom rjade, dostavljajuščem predel’nye veličiny integralov pri razloženii podintegral’noĭ funkcii na množeteli, Priloženi k 57 tomu Zapisok Imp. Akad. Nauk, 4Search in Google Scholar

[8] P. Cerone, On a Čebyšev-type functional and Güss-like bounds, Math. Inequal. Appl., 9 (1), (2006), 87-10210.7153/mia-09-09Search in Google Scholar

[9] P. Cerone, On Chebyshev functional bounds, Diérential & diérence equations and applications, (2006), 267-277Search in Google Scholar

[10] P. Cerone, On some results involving the Čebyšev functional and its generalisations, J. Inequal. Pure Appl. Math., 4 (3, Article 55), (2003), 17 pp.Search in Google Scholar

[11] P. Cerone and S. S. Dragomir, A refinement of the Güss inequality and applications, Tamkang J. Math., 38 (1), (2007), 37-4910.5556/j.tkjm.38.2007.92Search in Google Scholar

[12] P. Cerone and S. S. Dragomir, Chebychev functional bounds using Ostrowski seminorms, Southeast Asian Bull. Math., 28 (2), (2004), 219-228Search in Google Scholar

[13] P. Cerone and S. S. Dragomir, New bounds for the Čebyšev functional, Appl. Math. Lett., 18 (6), (2005), 603-61110.1016/j.aml.2003.09.013Search in Google Scholar

[14] S. S. Dragomir, Inequalities for the Čebyšev functional of two functions of selfadjoint operators in Hilbert spaces, Aust. J. Math. Anal. & Appl., 6 (1, Article 7), (2009), 1-58Search in Google Scholar

[15] S. S. Dragomir, Some inequalities for power series of selfadjoint operators in Hilbert spaces via reverses of the Schwarz inequality, Integral Transforms Spec. Funct., 20 (9-10), (2009), 757-76710.1080/10652460902910054Search in Google Scholar

[16] S. S. Dragomir, Inequalities for power series in Banach Algebras, SUT J. of Math., 50 (1), (2014), 25-4510.1186/1029-242X-2014-294Search in Google Scholar

[17] S. S. Dragomir, On some improvements of Čebyšev’s inequality for sequences and integrals, Studia Univ. Babeš-Bolyai, Mathematica (Romania), XXXV (4), (1990), 35-40Search in Google Scholar

[18] S. S. Dragomir, Some improvement of Čebyšev’s inequality for isotonic functionals, Atti. Sem. Mat. Fis. Univ. Modena (Italy), 41, (1993), 473-481Search in Google Scholar

[19] S.S. Dragomir, A generalization of Güss’ inequality in inner product spaces and applications, 237, (1999), 74-8210.1006/jmaa.1999.6452Search in Google Scholar

[20] S. S. Dragomir, Some discrete inequalities of Güss type and applications in guessing theory, Honam Math. J., 21 (1), (1999), 145-156Search in Google Scholar

[21] S. S. Dragomir, Güss inequality in inner product spaces, The Australian Math Soc. Gazette, 26 (2), (1999), 66-70Search in Google Scholar

[22] S. S. Dragomir, A Güss type integral inequality for mappings of r-Hölder’s type and applications for trapezoid formula, Tamkang J. of Math., 31 (1), (2000), 43-4710.5556/j.tkjm.31.2000.413Search in Google Scholar

[23] S.S. Dragomir, Some integral inequalities of Güss type, Indian J. of Pure and Appl. Math., 31 (4), (2000), 397-41510.1155/S1025583400000084Search in Google Scholar

[24] RS. S. Dragomir, On the Ostrowski inequality for the Riemann-Stieltjes integral R 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), 35-45Search in Google Scholar

[25] S. S. Dragomir, Some Güss type inequalities in inner product spaces, J. Inequal. Pure & Appl. Math., 4 (2), (2003), Article 42, (Online: http://jipam.vu.edu.au/article.php?sid=280)Search in Google Scholar

[26] S. S. Dragomir, Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces, J. Inequal. Pure & Appl. Math., 5 (3), (2004), Article 76. (Online: http://jipam.vu.edu.au/article.php?sid=432)Search in Google Scholar

[27] S.S. Dragomir, New reverses of Schwarz, triangle and Bessel inequalities in inner product spaces, Austral. J. Math. Anal. & Applics., 1 (1), (2004), Article 1. (Online: http://ajmaa.org/cgi-bin/paper.pl?string=nrstbiips.tex )Search in Google Scholar

[28] S. S. Dragomir, On the Čebyšev’s inequality for weighted means, Acta Math. Hungar., 104 (4), (2004), 345-35510.1023/B:AMHU.0000036294.17857.c3Search in Google Scholar

[29] S.S. Dragomir, On Bessel and Güss inequalities for orthornormal families in inner product spaces, Bull. Austral. Math. Soc., 69 (2), (2004), 327-34010.1017/S0004972700036066Search in Google Scholar

[30] S. S. Dragomir, Advances in Inequalities of the Schwarz, Güss and Bessel Type in Inner Product Spaces, Nova Science Publishers Inc, New York, 2005Search in Google Scholar

[31] S. S. Dragomir, Reverses of the Schwarz inequality in inner product spaces generalising a Klamkin-McLenaghan result, Bull. Austral. Math. Soc., 73 (1), (2006), 69-7810.1017/S0004972700038636Search in Google Scholar

[32] S. S. Dragomir, Some new Güss’ type inequalities for functions of selfadjoint operators in Hilbert spaces, RGMIA Res. Rep. Coll., 11 (e), (2008), Art. 12Search in Google Scholar

[33] S. S. Dragomir, Inequalities for the Čebyšev functional of two functions of selfadjoint operators in Hilbert spaces, RGMIA Res. Rep. Coll., 11 (e), (2008), Art. 17Search in Google Scholar

[34] S. S. Dragomir, Some inequalities for the Čebyšev functional of two functions of selfadjoint operators in Hilbert spaces, RGMIA Res. Rep. Coll., 11 (e), (2008), Art. 8Search in Google Scholar

[35] S. S. Dragomir, Springer Briefs in Mathematics. Springer, New York, 2012Search in Google Scholar

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

[37] S. S. Dragomir, M. V. Boldea, C. Buše, and M. Megan, Norm inequalities of Čebyšev type for power series in Banach algebras, J. Inequal. Appl., 2014, 2014:29410.1186/1029-242X-2014-294Search in Google Scholar

[38] S. S. Dragomir, M. V. Boldea, and M. Megan, New bounds for Čebyšev functional for power series in Banach algebras via a Güss’-Lupaš type inequality, Preprint RGMIA Res. Rep. Coll., 17, (2014)10.1186/1029-242X-2014-294Search in Google Scholar

[39] S. S. Dragomir and G.L. Booth, On a Güss-Lupaš type inequality and its applications for the estimation of p-moments of guessing mappings, Mathematical Communications, 5, (2000), 117-126Search in Google Scholar

[40] S. S. Dragomir and I. Fedotov, An inequality of Güss’ type for Riemann-Stieltjes integral and applications for special means, Tamkang J. of Math., 29 (4), (1998), 286-29210.5556/j.tkjm.29.1998.4257Search in Google Scholar

[41] S. S. Dragomir and B. Mond, Some mappings associated with Čebyšev’s inequality for sequences of real numbers, Bull. Allahabad Math. Soc., 8/9, (1993/94), 37-55Search in Google Scholar

[42] S.S. Dragomir and J.E. Pečarič, Refinements of some inequalities for isotonic linear functionals, L’Anal. Num. Théor de L’Approx.(Romania), 18 (1), (1989), 61-65Search in Google Scholar

[43] S. S. Dragomir, J. Pečarič, and J. Sàndor, The Chebyshev inequality in pre- Hilbertian spaces. II., Proceedings of the Third Symposium of Mathematics and its Applications (Timişoara, 1989), (1990), 75-78Search in Google Scholar

[44] S. S. Dragomir and J. Sàndor, The Chebyshev inequality in pre-Hilbertian spaces. I., Proceedings of the Second Symposium of Mathematics and its Applications (Timişoara, 1987), (1988), 61{64Search in Google Scholar

[45] A. M. Fink, A treatise on Güss’ inequality, Analytic and Geometric Inequalities, Math. Appl., 478, (1999), 93-11310.1007/978-94-011-4577-0_7Search in Google Scholar

[46] G. Güss, Über das Maximum des absoluten Betrages von 1/b-a R b a f(x)g(x)dx -1/(b-a)2 R b a f(x)dx R b a g(x)dx, Math. Z., 39, (1935), 215-22610.1007/BF01201355Search in Google Scholar

[47] Z. Liu, Refinement of an inequality of Güss type for Riemann-Stieltjes integral, Soochow J. Math., 30 (4), (2004), 483-489Search in Google Scholar

[48] A. Matkovič, J. Pečarič, and I. Perič, A variant of Jensen’s inequality of Mercer’s type for operators with applications, Linear Algebra Appl., 418 (2-3), (2006), 551-56410.1016/j.laa.2006.02.030Search in Google Scholar

[49] D. S. Mitrinovič and J.E. Pečarič, History, variations and generalizations of the Čebyšev inequality and question of some priorities. II, Rad Jugoslav. Akad. Znan. Umjet. No., 450, (1990), 139-156Search in Google Scholar

[50] D. S. Mitrinovič and J.E. Pečarič, On an identity of D.Z. Djokovič, Prilozi Mak. Akad.Nauk. Umj. (Skopje), 12 (1), (1991), 21-22Search in Google Scholar

[51] D. S. Mitrinovič and P.M. Vasič, History, variations and generalisations of the Čebyšev inequality and the question of some priorities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 461{497, (1974), 1-30Search in Google Scholar

[52] B. G. Pachpatte, A note on Čebyšev type inequalities, An. Sfitiintfi. Univ. Al. I. Cuza Iaši. Mat. (N.S.)(Romania), 53 (1), (2007), 97-102Search in Google Scholar

[53] B. G. Pachpatte, New Čebyšev type inequalities involving functions of two and three variables, Soochow J. Math., 33 (4), (2007), 569-577Search in Google Scholar

[54] B. G. Pachpatte, A note on Güss type inequalities via Cauchy’s mean value theorem, Math. Inequal. Appl., 11 (1), (2008), 75-8010.7153/mia-11-04Search in Google Scholar

[55] J. Pečarič, Remarks on Biernacki’s generalization of Čebyšev’s inequality, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 47, (1993), 116-122Search in Google Scholar

[56] J. E. Pečarič and S.S. Dragomir, Some remarks on Čebyšev’s inequality, L’Anal. Num. Théor de L’Approx., 19 (1), (1990), 58-65Search in Google Scholar

[57] C.-J. Zhao and W.-S. Cheung, On multivariate Güss inequalities, J. Inequal. Appl., 2008, Art. ID 249438, 8 pp. 10.1155/2008/249438Search in Google Scholar

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