##### Title: Two-Point Fuzzy Ostrowski Type Inequalities

##### Pages: 35-46

##### Cite as:

Muhammad Amer Latif, Sabir Hussain, Two-Point Fuzzy Ostrowski Type Inequalities, Int. J. Anal. Appl., 3 (1) (2013), 35-46.#### Abstract

Two-point fuzzy Ostrowski type inequalities are proved for fuzzy Hölder and fuzzy differentiable functions. The two-point fuzzy Ostrowski type inequality for M-lipshitzian mappings is also obtained. It is proved that only the two-point fuzzy Ostrowski type inequality for M-lipshitzian mappings is sharp and as a consequence generalize the two-point fuzzy Ostrowski type inequalities obtained for fuzzy differentiable functions.

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#### References

- George A. Anastassiou, Ostrowski type inequalities, Proc. AMS, 123 (1995), 3775–3791.
- George A. Anastassiou, Fuzzy Ostrowski type inequalities, Computational and Applied Mathematics,Vol. 22, No. 2 (2003), pp. 279-292.
- George A. Anastassiou, Univariate fuzzy-random neural network approximation operators,Computers & Mathematics with Applications Volume 48, Issue 9, November 2004, Pages1263-1283.
- George A. Anastassiou and Sorin Gal, On a fuzzy trigonometric approximation theorem ofWeierstrass-type, Journal of Fuzzy Mathematics, 9, No. 3 (2001), 701–708.
- N. S. Barnett and S. S. Dragomir, Issues of estimating in the monitoring of constant flowconinuous streams, RGMIA, Research report collection, Vol. 2, No. 3 (1999), pp.275-282.
- A.M. Fink, Bounds on the deviation of a function from its averages, Czechoslavak Math. J.,42 (117) (1992), 289–310.
- S. Gal, Approximation theory in fuzzy setting, Chapter 13 in Handbook of Analytic ComputationalMethods in Applied Mathematics (edited by G. Anastassiou), Chapman & Hall,CRC Press, Boca Raton, NewYork, 2000, pp. 617–666.
- A. Ostrowski, Uber die Absolutabweichung einer differentiebaren Funktion von ihrem Inte- ¨gralmittelwert, Comment. Math. Helv., 10 (1938), 226–227. Comp. Appl. Math., Vol. 22, N.2, 2003.
- M. Mati´c and J. Peˇcari´c, Two-pont Ostrowski inequality, Mathematical Inequalities & Applications,4 2(2001), 215-221.
- M.L. Puri and D.A. Ralescu, Differentials of fuzzy functions, J. of Math. Analysis and Appl.,91 (1983), 552–558.
- CongxinWu and Zengtai Gong, On Henstock integral of fuzzy number valued functions (I),Fuzzy Sets and Systems, 120, No. 3 (2001), 523–532.
- L.A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353.