New Generalized Inequalities for Functions of Bounded Variation

Hüseyin Budak; Mehmet Zeki Sarıkaya

doi:10.17776/csj.414037

EN TR

New Generalized Inequalities for Functions of Bounded Variation

Abstract

In this paper, firstly we obtain some generalized trapezoid and midpoint type inequalities for functions of bounded variation using two new generalized identities for Riemann-Stieltjes integrals. Then quadrature formula is also provided.

Keywords

Functions of bounded variation,Ostrowski type inequalities,Riemann-Stieltjes integrals,Riemann-Stieltjes integrals

References

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[2]. Budak H. and Sarikaya M.Z., New weighted Ostrowski type inequalities for mappings with first derivatives of bounded variation TJMM, 8-1(2016) 21-27.
[3]. Budak H. and Sarikaya M.Z., Sarikaya, New weighted Ostrowski type inequalities for mappings whose nth derivatives are of bounded variation, International Journal of Analysis and Applications, 12-1(2016) 71-79.
[4]. Budak H., Sarikaya M.Z., Akkurt A. and Yildirim H., Perturbed companion of Ostrowski type inequality for functions whose first derivatives are of bounded variation, Konuralp Journal of Mathematics, 5-1(2017) 161-175.
[5]. Budak H. and Sarikaya M.Z., A new Ostrowski type inequalities for functions whose first derivatives are bounded variation, Moroccan Journal of Pure and Applied Analysis, 2-1(2016) 1-11.
[6]. Budak H., Sarikaya M.Z., and Qayyum A., Improvement in companion of Ostrowski type inequalities for mappings whose first derivatives are of bounded variation and application, Filomat, 31-16(2017) 5305–5314.
[7]. Cerone P., Cheung W.S., and Dragomir S.S., On Ostrowski type inequalities for Stieltjes integrals with absolutely continuous integrands and integrators of bounded variation, Computers and Mathematics with Applications 54 (2007) 183-191.
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[13]. Dragomir S.S., Refinements of the generalized trapezoid and Ostrowski inequalities for functions of bounded variation. Arch. Math. (Basel) 91-5(2008) 450-460.
[14]. Dragomir S.S. and Momoniat E., A three point quadrature rule for functions of bounded variation and applications, RGMIA Research Report Collection, 14(2011) Article 33, 16 pp.
[15]. Ostrowski A.M., Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10(1938) 226-227.
[16]. Tseng K-L, Yang G-S, and Dragomir S. S., Generalizations of weighted trapezoidal inequality for mappings of bounded variation and their applications, Mathematical and Computer Modelling 40 (2004) 77-84.
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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Hüseyin Budak ^*
Türkiye

Mehmet Zeki Sarıkaya
Türkiye

Publication Date

September 30, 2018

Submission Date

April 10, 2018

Acceptance Date

September 11, 2018

Published in Issue

Year 2018 Volume: 39 Number: 3

DOI

https://doi.org/10.17776/csj.414037

IZ

https://izlik.org/JA57TU85TT

Cite

RIS / Bibtex

APA

Budak, H., & Sarıkaya, M. Z. (2018). New Generalized Inequalities for Functions of Bounded Variation. Cumhuriyet Science Journal, 39(3), 668-678. https://doi.org/10.17776/csj.414037

New Generalized Inequalities for Functions of Bounded Variation

New Generalized Inequalities for Functions of Bounded Variation

Abstract

Keywords

Sınırlı Varyasyonlu Fonksiyonlar için Yeni Genelleşmiş Eşitsizlikler

Öz

Anahtar Kelimeler

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite