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PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION

Year 2017, Volume: 5 Issue: 1, 161 - 175, 01.04.2017

HÜSEYİN Budak , MEHMET ZEKİ Sarıkaya , ABDULLAH Akkurt , HÜSEYİN Yıldırım

Abstract

In this paper, some perturbed companions of Ostrowski type integral inequalities for functions whose rst derivatives are of bounded variation are established.

Keywords

Perturbed Ostrowski type inequality Function of bounded variation.

References

  • [1] M. W. Alomari, A Generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation, RGMIA Research Report Collection, 14(2011), Article 87, 11 pp.
  • [2] M. W. Alomari and M.A. Latif, Weighted companion for the Ostrowski and the generalized trapezoid inequalities for mappings of bounded variation, RGMIA Research Report Collection, 14(2011), Article 92, 10 pp.
  • [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] H. Budak and M.Z. Sarikaya, On generalization of Dragomir's inequalities, RGMIA Research Report Collection, 17(2014), Article 155, 10 pp.
  • [5] H. Budak and M.Z. Sarikaya, New weighted Ostrowski type inequalities for mappings with rst derivatives of founded variation, RGMIA Research Report Collection, 18(2015), Article 43, 8 pp.
  • [6] H. Budak and M.Z. Sarikaya, A new generalization of Ostrowski type inequality for mappings of bounded variation, RGMIA Research Report Collection, 18(2015), Article 47, 9 pp.
  • [7] H. Budak and M.Z. Sarikaya, On generalization of weighted Ostrowski type inequalities for functions of bounded variation, RGMIA Research Report Collection, 18(2015), Article
  • [8] H. Budak and M. Z. Sarikaya, A new Ostrowski type inequality for functions whose fi rst derivatives are of bounded variation, Moroccan J. Pure Appl. Anal., 2(1)(2016), 1-11.
  • [9] H. Budak and M.Z. Sarikaya, A companion of Ostrowski type inequalities for mappings of bounded variation and some applications, RGMIA Research Report Collection, 19(2016), Article 24, 10 pp.
  • [10] H. Budak, M.Z. Sarikaya and A. Qayyum, Improvement in companion of Ostrowski type inequalities for mappings whose rst derivatives are of bounded variation and application, RGMIA Research Report Collection, 19(2016), Article 25, 11 pp.
  • [11] H. Budak, M.Z. Sarikaya and S.S. Dragomir, Some perturbed Ostrowski type inequality for twice differentiable functions, RGMIA Research Report Collection, 19 (2016), Article 47, 14 pp.
  • [12] H. Budak and M. Z. Sarikaya, Some perturbed Ostrowski type inequality for functions whose rst derivatives are of bounded variation, RGMIA Research Report Collection, 19 (2016), Article 54, 13 pp.
  • [13] S. S. Dragomir and N.S. Barnett, An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection, 1(2)(1998) :
  • [14] S. S. Dragomir, The Ostrowski integral inequality for mappings of bounded variation, Bulletin of the Australian Mathematical Society, 60(1) (1999), 495-508.
  • [15] S. S. Dragomir, and A. Sofo, An integral inequality for twice di erentiable mappings and application, Tamkang J. Math., 31(4) 2000.
  • [16] S. S. Dragomir, On the Ostrowski's integral inequality for mappings with bounded variation and applications, Mathematical Inequalities & Applications, 4 (2001), no. 1, 59{66.
  • [17] S. S. Dragomir, A companion of Ostrowski's inequality for functions of bounded variation and applications, International Journal of Nonlinear Analysis and Applications, 5 (2014) No. 1, 89-97 pp.
  • [18] S. S. Dragomir, Some perturbed Ostrowski type inequalities for functions of bounded variation, Preprint RGMIA Research Report Collection, 16 (2013), Art. 93.
  • [19] S. S. Dragomir, Approximating real functions which possess nth derivatives of bounded variation and applications, Computers and Mathematics with Applications 56 (2008) 2268-2278.
  • [20] S. S. Dragomir, Some perturbed Ostrowski type inequalities for functions of bounded variation, Asian-European Journal of Mathematics, 8(4)(2015; ),14 pages. DOI:10.1142/S1793557115500692
  • [21] S. S. Dragomir, Some Perturbed Ostrowski Type Inequalities for Absolutely Continuous Functions (I), Acta Universitatis Matthiae Belii, series Mathematics 23(2015), 71{86.
  • [22] S. S. Dragomir, Some Perturbed Ostrowski Type Inequalities for Absolutely Continuous Functions (II), RGMIA Research Report Collection, 16(2013), Article 93, 16 pp.
  • [23] S. S. Dragomir, Some Perturbed Ostrowski Type Inequalities for Absolutely Continuous Functions (III), TJMM, 7(1)(2015),31-43.
  • [24] S. S. Dragomir, Perturbed Companions of Ostrowski's Inequality for Functions of Bounded Variation, RGMIA Research Report Collection, 17(2014), Article 1, 16 pp.
  • [25] S. S. Dragomir, Perturbed Companions of Ostrowski's Inequality for Absolutely Continuous Functions (I), RGMIA Research Report Collection, 17(2014), Article 7, 15 pp.
  • [26] S. S. Dragomir, Perturbed Companions of Ostrowski's Inequality for Absolutely Continuous Functions (II), GMIA Research Report Collection, 17(2014), Article 19, 11 pp.
  • [27] W. Liu and Y. Sun, A Re nement of the Companion of Ostrowski inequality for functions of bounded variation and Applications, arXiv:1207.3861v1, (2012).
  • [28] Z. Liu, Some Ostrowski type inequalities, Mathematical and Computer Modelling 48 (2008) 949{960.
  • [29] A. M. Ostrowski,  Uber die absolutabweichung einer di erentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10(1938), 226-227.
  • [30] J. Park, Some Companions of an Ostrowski-like Type Inequality for Twice Differentiable Functions, Applied Mathematical Sciences, Vol. 8, 2014, no. 47, 2339 - 2351.
  • [31] M. Liu, Y. Zhu and J. Park, Some companions of perturbed Ostrowski-type inequalities based on the quadratic kernel function with three sections and applications, J. of Ineq. and Applications, 2013 2013:226.
  • [32] A. Ra q, N.A. Mir and F. Zafar, A generalized Ostrowski-Gruss Type inequality for twice differentiable mappings and application, JIPAM, 7(4)(2006), article 124.
  • [33] M. Z. Sarikaya, On the Ostrowski type integral inequality, Acta Mathematica Universitatis Comenianae, Vol. LXXIX, 1(2010);129-134.
  • [34] M. Z. Sarikaya and E. Set, On New Ostrowski Type Integral Inequalities, Thai Journal of Mathematics, 12(1)(2014) 145-154.
  • [35] M. Z. Sarikaya, H. Budak, T. Tunc, S. Erden and H. Yaldiz, Perturbed companion of Ostrowski type inequality for twice differentiable functions, Facta Universitatis, Series: Mathematics and Informatics, Vol. 31, No 3 (2016), 593-607.
  • [36] E. Set and M. Z. Sarikaya, On a new Ostrowski-type inequality and related results, Kyungpook Mathematical Journal, 54(2014), 545-554.
  • [37] A. Qayyum, M. Shoaib and I. Faye, Companion of Ostrowski-type inequality based on 5-step quadratic kernel and pplications, Journal of Nonlinear Science and Applications, 9 (2016), 537-552.
  • [38] A. Qayyum, M. Shoaib and I. Faye, On new re nements and applications of effcient quadrature rules using n-times differentiable mappings, RGMIA Research Report Collection, 19(2016), Article 9, 22 pp.

Year 2017, Volume: 5 Issue: 1, 161 - 175, 01.04.2017

HÜSEYİN Budak , MEHMET ZEKİ Sarıkaya , ABDULLAH Akkurt , HÜSEYİN Yıldırım

Abstract

References

  • [1] M. W. Alomari, A Generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation, RGMIA Research Report Collection, 14(2011), Article 87, 11 pp.
  • [2] M. W. Alomari and M.A. Latif, Weighted companion for the Ostrowski and the generalized trapezoid inequalities for mappings of bounded variation, RGMIA Research Report Collection, 14(2011), Article 92, 10 pp.
  • [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] H. Budak and M.Z. Sarikaya, On generalization of Dragomir's inequalities, RGMIA Research Report Collection, 17(2014), Article 155, 10 pp.
  • [5] H. Budak and M.Z. Sarikaya, New weighted Ostrowski type inequalities for mappings with rst derivatives of founded variation, RGMIA Research Report Collection, 18(2015), Article 43, 8 pp.
  • [6] H. Budak and M.Z. Sarikaya, A new generalization of Ostrowski type inequality for mappings of bounded variation, RGMIA Research Report Collection, 18(2015), Article 47, 9 pp.
  • [7] H. Budak and M.Z. Sarikaya, On generalization of weighted Ostrowski type inequalities for functions of bounded variation, RGMIA Research Report Collection, 18(2015), Article
  • [8] H. Budak and M. Z. Sarikaya, A new Ostrowski type inequality for functions whose fi rst derivatives are of bounded variation, Moroccan J. Pure Appl. Anal., 2(1)(2016), 1-11.
  • [9] H. Budak and M.Z. Sarikaya, A companion of Ostrowski type inequalities for mappings of bounded variation and some applications, RGMIA Research Report Collection, 19(2016), Article 24, 10 pp.
  • [10] H. Budak, M.Z. Sarikaya and A. Qayyum, Improvement in companion of Ostrowski type inequalities for mappings whose rst derivatives are of bounded variation and application, RGMIA Research Report Collection, 19(2016), Article 25, 11 pp.
  • [11] H. Budak, M.Z. Sarikaya and S.S. Dragomir, Some perturbed Ostrowski type inequality for twice differentiable functions, RGMIA Research Report Collection, 19 (2016), Article 47, 14 pp.
  • [12] H. Budak and M. Z. Sarikaya, Some perturbed Ostrowski type inequality for functions whose rst derivatives are of bounded variation, RGMIA Research Report Collection, 19 (2016), Article 54, 13 pp.
  • [13] S. S. Dragomir and N.S. Barnett, An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection, 1(2)(1998) :
  • [14] S. S. Dragomir, The Ostrowski integral inequality for mappings of bounded variation, Bulletin of the Australian Mathematical Society, 60(1) (1999), 495-508.
  • [15] S. S. Dragomir, and A. Sofo, An integral inequality for twice di erentiable mappings and application, Tamkang J. Math., 31(4) 2000.
  • [16] S. S. Dragomir, On the Ostrowski's integral inequality for mappings with bounded variation and applications, Mathematical Inequalities & Applications, 4 (2001), no. 1, 59{66.
  • [17] S. S. Dragomir, A companion of Ostrowski's inequality for functions of bounded variation and applications, International Journal of Nonlinear Analysis and Applications, 5 (2014) No. 1, 89-97 pp.
  • [18] S. S. Dragomir, Some perturbed Ostrowski type inequalities for functions of bounded variation, Preprint RGMIA Research Report Collection, 16 (2013), Art. 93.
  • [19] S. S. Dragomir, Approximating real functions which possess nth derivatives of bounded variation and applications, Computers and Mathematics with Applications 56 (2008) 2268-2278.
  • [20] S. S. Dragomir, Some perturbed Ostrowski type inequalities for functions of bounded variation, Asian-European Journal of Mathematics, 8(4)(2015; ),14 pages. DOI:10.1142/S1793557115500692
  • [21] S. S. Dragomir, Some Perturbed Ostrowski Type Inequalities for Absolutely Continuous Functions (I), Acta Universitatis Matthiae Belii, series Mathematics 23(2015), 71{86.
  • [22] S. S. Dragomir, Some Perturbed Ostrowski Type Inequalities for Absolutely Continuous Functions (II), RGMIA Research Report Collection, 16(2013), Article 93, 16 pp.
  • [23] S. S. Dragomir, Some Perturbed Ostrowski Type Inequalities for Absolutely Continuous Functions (III), TJMM, 7(1)(2015),31-43.
  • [24] S. S. Dragomir, Perturbed Companions of Ostrowski's Inequality for Functions of Bounded Variation, RGMIA Research Report Collection, 17(2014), Article 1, 16 pp.
  • [25] S. S. Dragomir, Perturbed Companions of Ostrowski's Inequality for Absolutely Continuous Functions (I), RGMIA Research Report Collection, 17(2014), Article 7, 15 pp.
  • [26] S. S. Dragomir, Perturbed Companions of Ostrowski's Inequality for Absolutely Continuous Functions (II), GMIA Research Report Collection, 17(2014), Article 19, 11 pp.
  • [27] W. Liu and Y. Sun, A Re nement of the Companion of Ostrowski inequality for functions of bounded variation and Applications, arXiv:1207.3861v1, (2012).
  • [28] Z. Liu, Some Ostrowski type inequalities, Mathematical and Computer Modelling 48 (2008) 949{960.
  • [29] A. M. Ostrowski,  Uber die absolutabweichung einer di erentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10(1938), 226-227.
  • [30] J. Park, Some Companions of an Ostrowski-like Type Inequality for Twice Differentiable Functions, Applied Mathematical Sciences, Vol. 8, 2014, no. 47, 2339 - 2351.
  • [31] M. Liu, Y. Zhu and J. Park, Some companions of perturbed Ostrowski-type inequalities based on the quadratic kernel function with three sections and applications, J. of Ineq. and Applications, 2013 2013:226.
  • [32] A. Ra q, N.A. Mir and F. Zafar, A generalized Ostrowski-Gruss Type inequality for twice differentiable mappings and application, JIPAM, 7(4)(2006), article 124.
  • [33] M. Z. Sarikaya, On the Ostrowski type integral inequality, Acta Mathematica Universitatis Comenianae, Vol. LXXIX, 1(2010);129-134.
  • [34] M. Z. Sarikaya and E. Set, On New Ostrowski Type Integral Inequalities, Thai Journal of Mathematics, 12(1)(2014) 145-154.
  • [35] M. Z. Sarikaya, H. Budak, T. Tunc, S. Erden and H. Yaldiz, Perturbed companion of Ostrowski type inequality for twice differentiable functions, Facta Universitatis, Series: Mathematics and Informatics, Vol. 31, No 3 (2016), 593-607.
  • [36] E. Set and M. Z. Sarikaya, On a new Ostrowski-type inequality and related results, Kyungpook Mathematical Journal, 54(2014), 545-554.
  • [37] A. Qayyum, M. Shoaib and I. Faye, Companion of Ostrowski-type inequality based on 5-step quadratic kernel and pplications, Journal of Nonlinear Science and Applications, 9 (2016), 537-552.
  • [38] A. Qayyum, M. Shoaib and I. Faye, On new re nements and applications of effcient quadrature rules using n-times differentiable mappings, RGMIA Research Report Collection, 19(2016), Article 9, 22 pp.
There are 38 citations in total.

Details

Subjects Engineering
Journal Section Research Article
Authors

HÜSEYİN Budak

MEHMET ZEKİ Sarıkaya

ABDULLAH Akkurt

HÜSEYİN Yıldırım

Submission Date March 9, 2017
Acceptance Date March 8, 2017
Publication Date April 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Budak, H., Sarıkaya, M. Z., Akkurt, A., Yıldırım, H. (2017). PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION. Konuralp Journal of Mathematics, 5(1), 161-175.
AMA Budak H, Sarıkaya MZ, Akkurt A, Yıldırım H. PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION. Konuralp J. Math. April 2017;5(1):161-175.
Chicago Budak, HÜSEYİN, MEHMET ZEKİ Sarıkaya, ABDULLAH Akkurt, and HÜSEYİN Yıldırım. “PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION”. Konuralp Journal of Mathematics 5, no. 1 (April 2017): 161-75.
EndNote Budak H, Sarıkaya MZ, Akkurt A, Yıldırım H (April 1, 2017) PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION. Konuralp Journal of Mathematics 5 1 161–175.
IEEE H. Budak, M. Z. Sarıkaya, A. Akkurt, and H. Yıldırım, “PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION”, Konuralp J. Math., vol. 5, no. 1, pp. 161–175, 2017.
ISNAD Budak, HÜSEYİN et al. “PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION”. Konuralp Journal of Mathematics 5/1 (April2017), 161-175.
JAMA Budak H, Sarıkaya MZ, Akkurt A, Yıldırım H. PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION. Konuralp J. Math. 2017;5:161–175.
MLA Budak, HÜSEYİN et al. “PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION”. Konuralp Journal of Mathematics, vol. 5, no. 1, 2017, pp. 161-75.
Vancouver Budak H, Sarıkaya MZ, Akkurt A, Yıldırım H. PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION. Konuralp J. Math. 2017;5(1):161-75.
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