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Some inequalities for weighted area balance via functions of bounded variation. (English) Zbl 1440.26019

Summary: We first define weighted area balance function. Then we prove two identities for the integrable functions involving weighted area balance. Moreover, using these equalities, we obtain some inequalities for mappings of bounded variation and for Lipschitzian functions, respectively.

MSC:

26D15 Inequalities for sums, series and integrals
26A45 Functions of bounded variation, generalizations
26D10 Inequalities involving derivatives and differential and integral operators
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References:

[1] M. W. Alomari, “A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation”, preprint 14, RGMIA Research Report Collection, 2011, https://rgmia.org/papers/v14/v14a87.pdf.
[2] M. W. Alomari, “A weighted companion for the Ostrowski and the generalized trapezoid inequalities for mappings of bounded variation”, preprint 14, RGMIA Research Report Collection, 2011, https://rgmia.org/papers/v14/v14a92.pdf.
[3] M. W. Alomari and S. S. Dragomir, “Mercer-Trapezoid rule for the Riemann-Stieltjes integral with applications”, Journal of Advances in Mathematics 2:2 (2013), 67-85.
[4] T. M. Apostol, Mathematical analysis, 2nd ed., Addison-Wesley, 1974.
[5] H. Budak and M. Z. Sarikaya, “A new Ostrowski type inequality for functions whose first derivatives are of bounded variation”, Moroccan J. Pure Appl. Anal. 2:1 (2016), 1-11. · Zbl 1339.26042
[6] H. Budak and M. Z. Sarikaya, “New weighted Ostrowski type inequalities for mappings with first derivatives of bounded variation”, Transylv. J. Math. Mech. 8:1 (2016), 21-27. · Zbl 1386.26015
[7] H. Budak and M. Z. Sarikaya, “A companion of Ostrowski type inequalities for mappings of bounded variation and some applications”, Trans. A. Razmadze Math. Inst. 171:2 (2017), 136-143. · Zbl 1373.26023
[8] H. Budak and M. Z. Sar\ikaya, “On generalization of Dragomir”s inequalities”, Turkish Journal of Analysis and Number Theory 5:5 (2017), 191-196.
[9] H. Budak and M. Z. Sarikaya, “A new generalization of Ostrowski type inequalities for mappings of bounded variation”, Lobachevskii J. Math. 39:9 (2018), 1320-1326. · Zbl 1408.26019
[10] H. Budak and M. Z. Sarikaya, “On generalization of weighted Ostrowski type inequalities for functions of bounded variation”, Asian-Eur. J. Math. 11:4 (2018), art. id. 1850049. · Zbl 1393.26023
[11] H. Budak, M. Z. Sarikaya, and A. Qayyum, “Improvement in companion of Ostrowski type inequalities for mappings whose first derivatives are of bounded variation and applications”, Filomat 31:16 (2017), 5305-5314.
[12] P. Cerone, S. S. Dragomir, and J. Roumeliotis, “An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications”, preprint 1, RGMIA Research Report Collection, 1998, https://rgmia.org/papers/v1n1/3res98.pdf. · Zbl 0957.41024
[13] S. S. Dragomir, “The Ostrowski integral inequality for mappings of bounded variation”, Bull. Austral. Math. Soc. 60:3 (1999), 495-508. · Zbl 0951.26011
[14] S. S. Dragomir, “On the Ostrowski”s integral inequality for mappings with bounded variation and applications”, Math. Inequal. Appl. 4:1 (2001), 59-66. · Zbl 1016.26017
[15] S. S. Dragomir, “Approximating real functions which possess \(n\) th derivatives of bounded variation and applications”, Comput. Math. Appl. 56:9 (2008), 2268-2278. · Zbl 1165.41324
[16] S. S. Dragomir, “Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation”, Arch. Math. \((\) Basel \() 91\):5 (2008), 450-460. · Zbl 1162.26005
[17] S. S. Dragomir, “A companion of Ostrowski”s inequality for functions of bounded variation and applications”, Int. J. Nonlinear Anal. Appl. 5:1 (2014), 89-97. · Zbl 1315.26020
[18] S. S. Dragomir, Aust. J. Math. Anal. Appl. 13:1 (2016), art. id. 5.
[19] S. S. Dragomir, “Inequalities for the area balance of absolutely continuous functions”, Stud. Univ. Babeş-Bolyai Math. 63:1 (2018), 37-57. · Zbl 1438.26052
[20] Z. Liu, “Some Ostrowski type inequalities”, Math. Comput. Modelling 48:5-6 (2008), 949-960. · Zbl 1156.26305
[21] M.
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