Research Article
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New Generalized Inequalities for Functions of Bounded Variation

Year 2018, Volume: 39 Issue: 3, 668 - 678, 30.09.2018

Hüseyin Budak , Mehmet Zeki Sarıkaya

https://doi.org/10.17776/csj.414037
https://izlik.org/JA57TU85TT

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]. 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]. 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.
  • [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]. Dragomir S.S., On trapezoid quadrature formula and applications, Kragujevac J. Math. 23(2001) 25-36.
  • [10]. Dragomir S.S., The Ostrowski integral inequality for mappings of bounded variation, Bull.Austral. Math. Soc., 60-1(1999) 495-508.
  • [11]. Dragomir S.S., On the midpoint quadrature formula for mappings with bounded variation and applications, Kragujevac J. Math. 22(2000) 13-19.
  • [12]. Dragomir S.S., On the Ostrowski's integral inequality for mappings with bounded variation and applications, Math. Inequal. Appl. 4-1 (2001) 59--66.
  • [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.
  • [17]. Tseng K-L, Improvements of some inequalities of Ostrowski type and their applications, Taiwan. J. Math. 12-9(2008) 2427-2441.
  • [18]. Tseng K-L, Improvements of the Ostrowski integral inequality for mappings of bounded variation II, Applied Mathematics and Computation 218 (2012) 5841-5847.
  • [19]. Tseng K-L and Hwang S-R, New Hermite-Hadamard-Type inequalities and their applications, Filomat 30-14(2016) 3667-3680.

Sınırlı Varyasyonlu Fonksiyonlar için Yeni Genelleşmiş Eşitsizlikler

Year 2018, Volume: 39 Issue: 3, 668 - 678, 30.09.2018

Hüseyin Budak , Mehmet Zeki Sarıkaya

https://doi.org/10.17776/csj.414037
https://izlik.org/JA57TU85TT

Abstract

Bu makalede ilk olarak Riemann-Stieltjes
integrallleri için genelleşmiş yeni iki eşitlik kullanılarak sınırlı
varyasyonlu fonksiyonlar için yamuk (trapezoid) ve orta nokta (midpoint) tipli
bazı genelleşmiş eşitsizlikler elde edilmiştir. Daha sonra karesel formül de
sağlanmıştır.

Keywords

Sınırlı varyasyonlu fonksiyon Ostrowski tipli eşitsizlikler Riemann-Stieltjes integralleri

References

  • [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]. 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.
  • [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]. Dragomir S.S., On trapezoid quadrature formula and applications, Kragujevac J. Math. 23(2001) 25-36.
  • [10]. Dragomir S.S., The Ostrowski integral inequality for mappings of bounded variation, Bull.Austral. Math. Soc., 60-1(1999) 495-508.
  • [11]. Dragomir S.S., On the midpoint quadrature formula for mappings with bounded variation and applications, Kragujevac J. Math. 22(2000) 13-19.
  • [12]. Dragomir S.S., On the Ostrowski's integral inequality for mappings with bounded variation and applications, Math. Inequal. Appl. 4-1 (2001) 59--66.
  • [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.
  • [17]. Tseng K-L, Improvements of some inequalities of Ostrowski type and their applications, Taiwan. J. Math. 12-9(2008) 2427-2441.
  • [18]. Tseng K-L, Improvements of the Ostrowski integral inequality for mappings of bounded variation II, Applied Mathematics and Computation 218 (2012) 5841-5847.
  • [19]. Tseng K-L and Hwang S-R, New Hermite-Hadamard-Type inequalities and their applications, Filomat 30-14(2016) 3667-3680.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Hüseyin Budak

Mehmet Zeki Sarıkaya

Submission Date April 10, 2018
Acceptance Date September 11, 2018
Publication Date September 30, 2018
DOI https://doi.org/10.17776/csj.414037
IZ https://izlik.org/JA57TU85TT
Published in Issue Year 2018 Volume: 39 Issue: 3

Cite

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

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