Refinements of Hermite-Hadamard Type Inequalities for s-Convex Functions with Applications to Special Means

Year 2021, Volume: 4 Issue: 3, 114 - 124, 30.09.2021

Uğur Selamet Kırmacı

https://doi.org/10.32323/ujma.953684

Cited By: 4

Abstract

In this paper, we establish some Hermite-Hadamard type inequalities for s-convex functions in the first and second sense. Some applications to special means for real numbers are also given.

Keywords

Hermite-Hadamard inequality , convex functions , s-convex functions , s-concave functions , Hölder inequality

References

• [1] M.W. Alomari, M. Darus, U.S. Kirmaci, Refinements of Hadamard type inequalities for quasi-convex functions with applictions to trapezoidal formula and to special means, Comput. Math. Appl. 59,1 (2010) 225-232.
• [2] M. W. Alomari, M. Darus, U. S. Kirmaci, Some inequalities of Hermite- Hadamard type for s-convex functions, Acta Math. Sci. Ser. B Eng. Ed. 31 (2011), 1643-1652.
• [3] S.S. Dragomir, R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998) 91–95.
• [4] S.S.Dragomir, Selected Topics on Hermite-Hadamard Inequalities and Applications, http://rgmia.vu.edu.au/SSDragomirWeb.html
• [5] S.S. Dragomir, S.Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math. 32 (4) (1999) 687-696.
• [6] S.S. Dragomir, On Simpson’s quadrature formula for Lipschitzian mappings and applications, Soochow J. Math. 25 (2) (1999) 175-180.
• [7] S.S. Dragomir, R.P. Agarwal, P.Cerone, On Simpson’s inequality and applications, J. Ineq. Appl. 5 (6) (2000) 533-579.
• [8] T. Du, Y. Li, Z. Yang, A generalization of simpson’s inequality via differentiable mapping using extended (s,m)-convex functions, Appl. Math. Comput. 293 (2017) 358-369.