The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.
References
[1]
Niculescu, C.P. and Persson, L.E. (2005) Convex Functions and Their Applications. CMS Books in Mathematics, Springer-Verlag.
[2]
Dragomir, S.S. and Pearce, C.E.M. (2000) Selected Topics on Hermitr-Hadamard Type Inequalities and Applications, RGMIA Monographs, Victoria University. http://rgmia.org/monographs/hermite_hadamard.html
[3]
Hudzik, H. and Maligranda, L. (1994) Some Remarks on s-Convex Functions. Aequationes Mathematicae, 48, 100-111. http://dx.doi.org/10.1007/BF01837981
[4]
Xi, B.Y. and Qi, F. (2015) Inequalities of Hermite-Hadamard Type for Extended s-Convex Functions and Applications to Means. Journal of Nonlinear and Convex Analysis, 16, 873-890.
[5]
Polyak, B.T. (1966) Existence Theorems and Convergence of Minimizing Sequences in Extremum Problems with Restrictions. Soviet Math.Dokl., 7, 72-75.
[6]
Hua, J., Xi, B.Y. and Qi, F. (2015) Some New Inequalities of Simpson Type for Strongly s-Convex Functions. Afrika Matematika, 26, 741-752. http://dx.doi.org/10.1007/s13370-014-0242-2
[7]
Dragomir, S.S. and Agarwal, R.P. (1998) Two Inequalities for Differentiable Mappings and Applications to Special Means of Real Numbers and to Trapezoidal Formula. Applied Mathematics Letters, 11, 91-95. http://dx.doi.org/10.1016/S0893-9659(98)00086-X
[8]
Kirmaci, U.S. (2004) Inequalities for Differentiable Mappings and Applications to Special Means of Real Numbers to Midpoint Formula. Applied Mathematics and Computation, 147, 137-146. http://dx.doi.org/10.1016/S0096-3003(02)00657-4
[9]
Sarikaya, M.Z., Set, E. and Özdemir, M.E. (2010) On New Inequalities of Simpson’s Type for s-Convex Functions. Computers & Mathematics with Applications, 60, 2191-2199. http://dx.doi.org/10.1016/j.camwa.2010.07.033.
