Research Article

New Generalized Inequalities for Functions of Bounded Variation

Volume: 39 Number: 3 September 30, 2018
Hüseyin Budak *, Mehmet Zeki Sarıkaya
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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

  1. [1]. Budak H. and Sarikaya M.Z., On generalization of Dragomir's inequalities, Turkish Journal of Analysis and Number Theory, 5-5(2017) 191-196.
  2. [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. [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. [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. [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. [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. [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.
  8. [8]. Cerone P., Dragomir S.S., and Pearce C.E.M., A generalized trapezoid inequality for functions of bounded variation, Turk J Math, 24 (2000) 147-163.
  9. [9]. Dragomir S.S., On trapezoid quadrature formula and applications, Kragujevac J. Math. 23(2001) 25-36.
  10. [10]. Dragomir S.S., The Ostrowski integral inequality for mappings of bounded variation, Bull.Austral. Math. Soc., 60-1(1999) 495-508.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

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
AMA
1.Budak H, Sarıkaya MZ. New Generalized Inequalities for Functions of Bounded Variation. CSJ. 2018;39(3):668-678. doi:10.17776/csj.414037
Chicago
Budak, Hüseyin, and Mehmet Zeki Sarıkaya. 2018. “New Generalized Inequalities for Functions of Bounded Variation”. Cumhuriyet Science Journal 39 (3): 668-78. https://doi.org/10.17776/csj.414037.
EndNote
Budak H, Sarıkaya MZ (September 1, 2018) New Generalized Inequalities for Functions of Bounded Variation. Cumhuriyet Science Journal 39 3 668–678.
IEEE
[1]H. Budak and M. Z. Sarıkaya, “New Generalized Inequalities for Functions of Bounded Variation”, CSJ, vol. 39, no. 3, pp. 668–678, Sept. 2018, doi: 10.17776/csj.414037.
ISNAD
Budak, Hüseyin - Sarıkaya, Mehmet Zeki. “New Generalized Inequalities for Functions of Bounded Variation”. Cumhuriyet Science Journal 39/3 (September 1, 2018): 668-678. https://doi.org/10.17776/csj.414037.
JAMA
1.Budak H, Sarıkaya MZ. New Generalized Inequalities for Functions of Bounded Variation. CSJ. 2018;39:668–678.
MLA
Budak, Hüseyin, and Mehmet Zeki Sarıkaya. “New Generalized Inequalities for Functions of Bounded Variation”. Cumhuriyet Science Journal, vol. 39, no. 3, Sept. 2018, pp. 668-7, doi:10.17776/csj.414037.
Vancouver
1.Hüseyin Budak, Mehmet Zeki Sarıkaya. New Generalized Inequalities for Functions of Bounded Variation. CSJ. 2018 Sep. 1;39(3):668-7. doi:10.17776/csj.414037

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