New generalized trapezoid type inequalities for complex functions defined on unit circle and applications

H. Budak

doi:10.37863/umzh.v72i12.6035

H. Budak Univ., D¨uzce, Turkey

DOI: https://doi.org/10.37863/umzh.v72i12.6035

Ключові слова: Function of bounded variation, trapezoid type inequalities, H¨older type condition, Riemann-Stieltjes integral

Анотація

UDC 517.5

Новi узагальненi нерiвностi типу трапецiї для комплексних функцiй на одиничному колi та їх застосування
За допомогою функцій обмеженої варіації та функцій, які задовольняють умову типу Гельдера, отримано нові узагальнені нерівності типу трапеції для комплексних функцій на одиничному колі.
З цих результатів також виведено квадратурну формулу.

Посилання

H. Budak, M. Z. Sarikaya, On generalization of Dragomir’s inequalities, Turkish J. Analysis and Number Theory, 5, № 5, 191 – 196 (2017).

H. Budak, M. Z. Sarikaya, A companion of Ostrowski type inequalities for mappings of bounded variation and some applications, Trans. A. Razmadze Math. Inst., 171, № 2, 136 – 143 (2017), https://doi.org/10.1016/j.trmi.2017.03.004 DOI: https://doi.org/10.1016/j.trmi.2017.03.004

H. Budak, M. Z. Sarikaya, A. Qayyum, New refinements and applications of Ostrowski type inequalities for mappings whose derivatives are of bounded variation, TWMS Journal of Applied and Eng. Math. (0000).

H. Budak, M. Z. Sarikaya, A. Qayyum, Improvement in companion of Ostrowski type inequalities for mappings whose first derivatives are of bounded variation and application, Filomat, 31, № 16, 5305 – 5314 (2017), https://doi.org/10.2298/fil1716305b DOI: https://doi.org/10.2298/FIL1716305B

P. Cerone, S. S. Dragomir, C. E. M. Pearce, A generalized trapezoid inequality for functions of bounded variation, Turkish J. Math., 24, № 2, 147 – 163 (2000).

S. S. Dragomir, The Ostrowski integral inequality for mappings of bounded variation, Bull.Austral. Math. Soc., 60, № 3, 495 – 508 (1999), https://doi.org/10.1017/S0004972700036662 DOI: https://doi.org/10.1017/S0004972700036662

S. S. Dragomir, On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Math. Inequal. and Appl., 4, № 1, 59 – 66 (2001), https://doi.org/10.7153/mia-04-05 DOI: https://doi.org/10.7153/mia-04-05

S. S. Dragomir, A companion of Ostrowski’s inequality for functions of bounded variation and applications, Int. J. Nonlinear Anal. and Appl., 5, № 1, 89 – 97 (2014).

S. S. Dragomir, Generalised trapezoid type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces, Mediterr. J. Math. 12, № 3, 573 – 591 (2015), https://doi.org/10.1007/s00009-014-0434-x DOI: https://doi.org/10.1007/s00009-014-0434-x

S. S. Dragomir, Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces, Arch. Math., 51, № 4, 233 – 254 (2015), https://doi.org/10.5817/AM2015-4-233 DOI: https://doi.org/10.5817/AM2015-4-233

S. S. Dragomir, trapezoid type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces, Georgian Math. J, 23, № 2, 199 – 210, 2016, https://doi.org/10.1515/gmj-2016-0012 DOI: https://doi.org/10.1515/gmj-2016-0012

Z. Liu, Some Companion of an Ostrowski type inequality and application, JIPAM, 10, № 2, Article 52, (2009), 12 p.

K.-L. Tseng, G.-S. Yang, S. S. Dragomir, Generalizations of weighted trapezoidal inequality for mappings of bounded variation and their applications, Math. and Comput. Modelling, 40, № 1-2, 77 – 84 (2004), https://doi.org/10.1016/j.mcm.2003.12.004 DOI: https://doi.org/10.1016/j.mcm.2003.12.004

K.-L. Tseng, Improvements of some inequalites of Ostrowski type and their applications, Taiwan. J. Math. 12, № 9, 2427 – 2441 (2008), https://doi.org/10.11650/twjm/1500405188 DOI: https://doi.org/10.11650/twjm/1500405188

K.-L. Tseng, S.-R. Hwang, G.-S. Yang, Y.-M. Chou, Improvements of the Ostrowski integral inequality for mappings of bounded variation I, Applied Math. and Comput., 217, 2348 – 2355 (2010), https://doi.org/10.1016/j.amc.2010.07.034 DOI: https://doi.org/10.1016/j.amc.2010.07.034

K.-L. Tseng, S.-R. Hwang, G.-S. Yang, Y.-M. Chou, Weighted Ostrowski integral inequality for mappings of bounded variation, Taiwanese J. of Math., 15, № 2, 573 – 585 (2011), https://doi.org/10.11650/twjm/1500406222 DOI: https://doi.org/10.11650/twjm/1500406222

K.-L. Tseng, Improvements of the Ostrowski integral inequality for mappings of bounded variation II, Applied Mathematics and Computation, 218, № 10, 5841 – 5847 (2012), https://doi.org/10.1016/j.amc.2011.11.047 DOI: https://doi.org/10.1016/j.amc.2011.11.047