INTEGRAL INEQUALITIES OF STEFFENSEN TYPE FOR SOME DIFFERENT CLASSES OF FUNCTIONS

Year 2023, Volume: 9 Issue: 2, 37 - 45, 31.12.2023

Erhan Set Emre Karaman Barış Çelik Ali Karaoğlan

Abstract

In this paper, we have obtained some new integral inequalities of Steffensen type for P-function and η-convex function with the help of identities proved by Mitrinovic et al..

Keywords

Convex function, η−convex function, P function, Steffensen inequality, Hermite-Hadamard inequality.

References

• ALOMARI, M.W., HUSSAIN, S., LIU, Z. (2017). Some Steffensen-type inequalities, Advances in Pure and Applied Mathematics, 8(3), 219-226.
• DRAGOMIR, S.S., PECARIC, J., PERSON, L.E. (1995). Some inequalities of Hadamard type, Soochow J. Math., 21(3), 335-341.
• DRAGOMIR, S.S., PEARCE, C.E.M. (2000). Selected Topics on Hermite-Hamadard Inequalities and Applications, Victoria University.
• DELAVAR, M.R. DRAGOMIR, S.S. (2017). On η-convexity, Mathematical Inequalities and Applications, 20(1), 203-216.
• HAYASHI, T. (1919). On curves with monotonous curvature, Têhoku Math. J., 15, 236-239.
• GORDJI, M.E., DELAVAR, M.R., DRAGOMIR, S.S. (2015). Some inequality related to η-convex function, RGMIA 18, Art. 8., 1-14.
• GORDJI, M.E., DRAGOMIR, S.S., DELAVAR, M.R. (2015). An inequality related to η-convex functions (II), Int. J. Nonlinear Anal. Appl., 6(2), 27-33.
• GORDJI, M.E., DELAVAR, M.R., DE LA SEN, M. (2016). On φ-convex functions, Journal of Mathematical Inequalities, 10(1), 173-183.
• MITRINOVIC, D.S., PECARIC, J.E., FINK, A.M. (1993). Classical and new inequalities in analysis, Kluwer, Dordrecht.
• STEFFENSEN, J.F. (1918). On certain inequalities between mean values and their application to actuarial problems, Scandinavian Actuarial Journal, 1918(1), 82-97.