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An application of Hayashi’s inequality for differentiable functions. (English) Zbl 0874.26017
It is shown that Iyengar’s inequality [{\it K. S. K. Iyengar}, Math. Stud. 6, 75-76 (1938)] can be obtained from the well-known generalization of Steffensen’s inequality for monotone functions obtained by {\it T. Hayashi} [Tôhoku Math. J. 15, 236-239 (1919; JFM 47.0222.03)].

26D15Inequalities for sums, series and integrals of real functions
26A51Convexity, generalizations (one real variable)
Full Text: DOI
[1] Mitrinović, D. S.; Pec\breve{}arić, J. E.; Fink, A. M.: Classical and new inequalities in analysis. (1993) · Zbl 0771.26009
[2] Mitrinović, D. S.; Pec\breve{}arić, J. E.; Fink, A. M.: Inequalities involving functions and their integrals and derivatives. (1991) · Zbl 0744.26011
[3] Dragomir, S. S.: Two mappings in connection to Hadamard’s inequality. J. math. Anal. appl. 167, 49-56 (1992) · Zbl 0758.26014