ON THE GENERALIZED INTEGRAL INEQUALITIES FOR TWICE DIFFERENTIABLE MAPPINGS

Key Findings & Data:Then, we establish several new inequalities for some twice differentiable mappings that are connected with the celebrated Hermite-Hadamard type and Ostrowski type integral inequalities.

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Conclusion & Impact:The results presented here would provide extensions of those given in earlier works

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Hermite-Hadamard inequality · Ostrowski inequality · Grüss inequality

Abstract

In this paper, an important integral equality is derived. Then, we establish several new inequalities for some twice differentiable mappings that are connected with the celebrated Hermite-Hadamard type and Ostrowski type integral inequalities. Some of the new inequalities are obtained by using Grüss inequality and Chebyshev inequality. The results presented here would provide extensions of those given in earlier works

Keywords

Hermite-Hadamard inequality Ostrowski inequality Grüss inequality Čebyšev inequality Hölder inequality.

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Cite This Article

SARIKAYA, M. Z., ERDEN, S., BUDAK, H. (2019). ON THE GENERALIZED INTEGRAL INEQUALITIES FOR TWICE DIFFERENTIABLE MAPPINGS. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 37 - Sayı: 1, 187–205. https://ajindex.com/articles/415051

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References (14)

F. Ahmad, N. S. Barnett and S. S. Dragomir, New Weighted Ostrowski and Cebysev Type Inequalities, Nonlinear Analysis: Theory, Methods & Appl., 71 (12), (2009), 1408-1412
F. Ahmad, A. Rafiq, N. A. Mir, Weighted Ostrowski type inequality for twice differentiable mappings, Global Journal of Research in Pure and Applied Math., 2 (2) (2006), 147-154
M. W. Alomari, A companion of Dragomir's generalization of Ostrowski's inequality and applications in numerical integration, Ukrainskij Matematytchnyj Zhurnal, 2012, Vol. 64, No. 4
N. S. Barnett and S. S. Dragomir, An Ostrowski type inequality for double integrals and applications for cubature formulae, Soochow J. Math., 27(1), (2001), 109-114
P. S. Bullen, Error estimates for some elementary quadrature rules, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 602-633 (1978), 97-103 (1979)
P. Cerone, S.S. Dragomir and J. Roumeliotis, An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection, Vol. 1, No. 1, 1998 Art.4
S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett., 11(5) (1998), 91-95
S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000
S. S. Dragomir, P. Cerone and J. Roumeliotis, A new generalization of Ostrowski's integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means, RGMIA Research Report Collection, Vol. 2, No. 1, 1999
S. S. Dragomir and A. Sofo, An integral inequality for twice differentiable mappings and applications, Tamk. J. Math., 31(4), 2000
S. S. Dragomir, P. Cerone and A. Sofo, Some remarks on the midpoint rule in numerical integration, RGMIA Research Report Collection, Vol. 1, No. 2, 1998. Art. 4 [12] T. S. Du, J. G. Liao, Y. J. Li, Properties and integral inequalities of Hadamard--Simpson type for the generalized -preinvex functions. J. Nonlinear Sci. Appl., 9, (2016), 3112-3126
T. S. Du, Y. J. Li, Z. Q. Yang, A generalization of Simpson's inequality via differentiable mapping using extended -convex functions. Appl. Math. Comput., 293, (2017), 358-369
G. Grüss, Über das maximum des absoluten Betrages von Math. Z., 39, 215-226, 1935
S. Hussain, M.A.Latif and M.