Inequalities for convex sequences and nondecreasing convex functions

1. Abramovich, S., Barić, J., Pečarić, J.: Fejer and Hermite-Hadamard type inequalities for superquadratic functions. J. Math. Anal. Appl. 344, 1048–1056 (2008)

   Article  MathSciNet  MATH  Google Scholar 

2. Borcea, J.: Equilibrium points of logarithmic potentials. Trans. Am. Math. Soc. 359, 3209–3237 (2007)

   Article  MATH  Google Scholar 

3. Breckner, W.W., Trif, T.: Convex Functions and Related Functional Equations: Selected Topics. Cluj University Press, Cluj (2008)

   MATH  Google Scholar 

4. Bullen, P.S.: Error estimates for some elementary quadrature rules. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 602–633, 97–103 (1978)

   MathSciNet  MATH  Google Scholar 

5. Burtea, A.-M.: Two examples of weighted majorization. An. Univ. Craiova Ser. Mat. Inform. 32(2), 92–99 (2010)

   MathSciNet  MATH  Google Scholar 

6. El Farissi, A.: Simple proof and refinement of Hermite–Hadamard inequality. J. Math. Inequal. 4(3), 365–369 (2010)

   Article  MathSciNet  MATH  Google Scholar 

7. Hammer, P.C.: The midpoint method of numerical integration. Math. Mag. 31, 193–195 (1957/1958)

8. Klaričić-Bakula, M., Pečarić, J., Perić, J.: Extensions of the Hermite–Hadamard inequality with applications. Math. Inequal. Appl. 12(4), 899–921 (2012)

   MathSciNet  MATH  Google Scholar 

9. Latreuch, Z., Belaïdi, B.: New inequalities for convex sequences with applications. Int. J. Open Problems Comput. Math. 5(3), 15–27 (2012)

   Article  Google Scholar 

10. Marshall, A.W., Olkin, I., Arnold, B.C.: Inequalities: Theory of Majorization and Its Applications, 2nd edn. Springer, New York (2011)

    Book  MATH  Google Scholar 

11. Minculete, N., Mitroi, F.-C.: Fejér-type inequalities. Austral. J. Math. Anal. Appl. 9(1), 1–8 (2012)

    MATH  Google Scholar 

12. Niezgoda, M.: An extension of results of A. McD. Mercer and I. Gavrea. J. Inequal. Pure Appl. Math. 6(4), Art. 107 (2005)

13. Niezgoda, M.: Sherman, Hermite-Hadamard and Fejér like inequalities for convex sequences and nondecreasing convex functions. Filomat (2016). (to appear)

14. Pereira, R., Plosker, S.: Dirichlet polynomials, majorization, and trumping. J. Phys. A 46, 80–86 (2015)

    MathSciNet  MATH  Google Scholar 

15. Sherman, S.: On a theorem of Hardy, Littlewood, Pólya, and Blackwell. Proc. Natl. Acad. Sci. USA 37(1), 826–831 (1957)

    MATH  Google Scholar 

16. Wu, S., Debnath, L.: Inequalities for convex sequences and their applications. Comput. Math. Appl. 54, 525–534 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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