Some additive reverses of Callebaut and Hölder inequalities for isotonic functionals
Some additive reverses of Callebaut and Hölder inequalities for isotonic functionals
In this paper, we obtain some reverses of Callebaut and Hölder inequalities for isotonic functionals via a reverse of Young’s inequality we have established recently. Applications for integrals and n-tuples of real numbers are provided as well.
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- D. Andrica, C. Badea: Grüss’ inequality for positive linear functionals, Periodica Math. Hung., 19 (1998), 155–167.
- P. R. Beesack, J. E. Peˇcari´c: On Jessen’s inequality for convex functions, J. Math. Anal. Appl., 110 (1985), 536–552.
- D. K. Callebaut: Generalization of Cauchy-Schwarz inequality, J. Math. Anal. Appl., 12 (1965), 491–494.
- S. S. Dragomir: A refinement of Hadamard’s inequality for isotonic linear functionals, Tamkang J. Math.(Taiwan), 24 (1992), 101–106.
- S. S. Dragomir: On a reverse of Jessen’s inequality for isotonic linear functionals, J. Ineq. Pure & Appl. Math., 2 (3) (2001), Article 36.
- S. S. Dragomir: On the Jessen’s inequality for isotonic linear functionals, Nonlinear Anal. Forum, 7 (2) (2002), 139–151.
- S. S. Dragomir: On the Lupa¸s-Beesack-Peˇcari´c inequality for isotonic linear functionals, Nonlinear Funct. Anal. & Appl., 7 (2) (2002), 285–298.
- S.S. Dragomir: Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc., 74 (3) (2006), 417–478.
- S. S. Dragomir: Additive refinements and reverses of Young’s operator inequality with applications, Preprint RGMIA Res. Rep. Coll., 18 (2015), Art. A 165.
- S. S. Dragomir: Inequalities for Synchronous Functions and Applications, Constr. Math. Anal., 2 (3) (2019), 109–123.
- S. S. Dragomir, Ostrowski’s Type Inequalities for the Complex Integral on Paths, Constr. Math. Anal., 3 (4) (2020), 125–138.
- S. S. Dragomir, N. M. Ionescu: On some inequalities for convex-dominated functions, L’Anal. Num. Théor. L’Approx., 19 (1) (1990), 21–27.
- S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University (2000).
- S. S. Dragomir, C. E. M. Pearce and J. E. Peˇcari´c: On Jessen’s and related inequalities for isotonic sublinear functionals, Acta. Sci. Math.(Szeged), 61 (1995), 373–382.
- S. Furuichi: Refined Young inequalities with Specht’s ratio, J. Egyptian Math. Soc., 20 (2012), 46–49.
- F. Kittaneh, Y. Manasrah: Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl., 361 (2010), 262–269.
- F. Kittaneh, Y. Manasrah: Reverse Young and Heinz inequalities for matrices, Linear Multilinear Algebra, 59 (2011), 1031–1037.
- W. Liao, J. Wu and J. Zhao: New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwanese J. Math., 19 (2) (2015), 467–479.
- A. Lupa¸s: A generalisation of Hadamard’s inequalities for convex functions, Univ. Beograd. Elek. Fak., 544/576 (1976), 115–121.
- J .E. Peˇcari´c: On Jessen’s inequality for convex functions (III), J. Math. Anal. Appl., 156 (1991), 231–239.
- J. E. Peˇcari´c, P. R. Beesack: On Jessen’s inequality for convex functions (II), J. Math. Anal. Appl., 118 (1986), 125–144.
- J. E. Peˇcari´c, S. S. Dragomir: A generalisation of Hadamard’s inequality for isotonic linear functionals, Radovi Mat.(Sarjevo), 7 (1991), 103–107.
- J. E. Peˇcari´c, I. Ra¸sa: On Jessen’s inequality, Acta. Sci. Math.(Szeged), 56 (1992), 305–309.
- W. Specht: Zer Theorie der elementaren Mittel, Math. Z., 74 (1960), 91–98.
- G. Toader, S. S. Dragomir: Refinement of Jessen’s inequality, Demonstr. Math., 28 (1995), 329–334.
- M. Tominaga: Specht’s ratio in the Young inequality, Sci. Math. Japon., 55 (2002), 583–588.
- G. Zuo, G. Shi and M. Fujii: Refined Young inequality with Kantorovich constant, J. Math. Inequal., 5 (2011), 551-556.