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

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.

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

Abstract

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

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.

Details

Subjects Engineering
Journal Section Articles
Authors

HÜSEYİN BUDAK
Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce
Türkiye


MEHMET ZEKİ SARIKAYA
Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce
Türkiye


ABDULLAH AKKURT
Department of Mathematics, Faculty of Science and Arts, University of Kahramanmaraş Sütçü İmam, 46100, Kahramanmaras
0000-0001-5644-1276
Türkiye


HÜSEYİN YILDIRIM
Department of Mathematics, Faculty of Science and Arts, University of Kahramanmaraş Sütçü İmam, 46100, Kahramanmaras
0000-0001-8855-9260
Türkiye

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

Cite

Bibtex @research article { konuralpjournalmath296988, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {}, publisher = {Mehmet Zeki SARIKAYA}, year = {2017}, volume = {5}, pages = {161 - 175}, doi = {}, title = {PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION}, key = {cite}, author = {Budak, HÜSEYİN and Sarıkaya, MEHMET ZEKİ and Akkurt, ABDULLAH and Yıldırım, HÜSEYİN} }
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 (KJM) , 5 (1) , 161-175 . Retrieved from https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/27713/296988
MLA Budak, H. , Sarıkaya, M. Z. , Akkurt, A. , Yıldırım, H. "PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION" . Konuralp Journal of Mathematics (KJM) 5 (2017 ): 161-175 <https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/27713/296988>
Chicago Budak, H. , Sarıkaya, M. Z. , Akkurt, A. , Yıldırım, H. "PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION". Konuralp Journal of Mathematics (KJM) 5 (2017 ): 161-175
RIS TY - JOUR T1 - PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION AU - HÜSEYİN Budak , MEHMET ZEKİ Sarıkaya , ABDULLAH Akkurt , HÜSEYİN Yıldırım Y1 - 2017 PY - 2017 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 161 EP - 175 VL - 5 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2017 ER -
EndNote %0 Konuralp Journal of Mathematics (KJM) PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION %A HÜSEYİN Budak , MEHMET ZEKİ Sarıkaya , ABDULLAH Akkurt , HÜSEYİN Yıldırım %T PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION %D 2017 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 5 %N 1 %R %U
ISNAD Budak, HÜSEYİN , Sarıkaya, MEHMET ZEKİ , Akkurt, ABDULLAH , Yıldırım, HÜSEYİN . "PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION". Konuralp Journal of Mathematics (KJM) 5 / 1 (April 2017): 161-175 .
AMA Budak H. , Sarıkaya M. Z. , 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): 161-175.
Vancouver Budak H. , Sarıkaya M. Z. , Akkurt A. , Yıldırım H. PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR FUNCTIONS WHOSE FIRST DERIVATIVES ARE OF BOUNDED VARIATION. Konuralp Journal of Mathematics (KJM). 2017; 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 Journal of Mathematics (KJM), vol. 5, no. 1, pp. 161-175, Apr. 2017
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