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The Jensen-Mercer Inequality with Infinite Convex Combinations

Year 2019, , 19 - 27, 30.04.2019
https://doi.org/10.36753/mathenot.559241

Abstract

The paper deals with discrete forms of double inequalities related to convex functions of one variable.
Infinite convex combinations and sequences of convex combinations are included. The double inequality
form of the Jensen-Mercer inequality and its variants are especially studied.

References

  • [1] Hadamard, J., Étude sur les propriétés des fonctions entières et en particulier d’une fonction considerée par Riemann, J. Math. Pures Appl., 58(1893), 171-215.
  • [2] Hermite, Ch., Sur deux limites d’une intégrale définie, Mathesis, 3(1883), 82.
  • [3] Iveli´c, S., Matkovic, A. and Pecaric, J. E., On a Jensen-Mercer operator inequality, Banach J. Math. Anal., 5(2011), 19-28.
  • [4] Jensen, J. L.W. V., Om konvekse Funktioner og Uligheder mellem Middelværdier, Nyt Tidsskr. Math. B, 16(1905), 49-68.
  • [5] Khan, M. A., Khan, G. A., Jameel, M., Khan, K. A. and Kilicman, A., New refinements of Jensen-Mercer’s inequality J. Comput. Theor. Nanosci., 12(2015), 4442-4449.
  • [6] Matkovic, A., Peˇcari´c, J. and Peri´c, I., A variant of Jensen’s inequality of Mercer’s type for operators with applications, Linear Algebra Appl., 418(2006), 551-564.
  • [7] Mercer, A. McD., A variant of Jensen’s inequality, JIPAM, 4(2003), Article 73.
  • [8] Niezgoda, M., A generalization of Mercer’s result on convex functions, Nonlinear Anal., 71(2009), 2771-2779.
  • [9] Pavic, Z., Convex function and its secant, Adv. Inequal. Appl., 2015(2015), Article 5.
  • [10] Pavic, Z., Generalizations of Jensen-Mercer’s inequality, J. Pure Appl. Math. Adv. Appl., 11(2014), 19-36.
  • [11] Pavic Z., Geometric and analytic connections of the Jensen and Hermite-Hadamard inequality, Math. Sci. Appl. E-Notes, 4(2016), 69-76.
  • [12] Pavic, Z., Inequalities with infinite convex combinations, submitted to FILOMAT.
Year 2019, , 19 - 27, 30.04.2019
https://doi.org/10.36753/mathenot.559241

Abstract

References

  • [1] Hadamard, J., Étude sur les propriétés des fonctions entières et en particulier d’une fonction considerée par Riemann, J. Math. Pures Appl., 58(1893), 171-215.
  • [2] Hermite, Ch., Sur deux limites d’une intégrale définie, Mathesis, 3(1883), 82.
  • [3] Iveli´c, S., Matkovic, A. and Pecaric, J. E., On a Jensen-Mercer operator inequality, Banach J. Math. Anal., 5(2011), 19-28.
  • [4] Jensen, J. L.W. V., Om konvekse Funktioner og Uligheder mellem Middelværdier, Nyt Tidsskr. Math. B, 16(1905), 49-68.
  • [5] Khan, M. A., Khan, G. A., Jameel, M., Khan, K. A. and Kilicman, A., New refinements of Jensen-Mercer’s inequality J. Comput. Theor. Nanosci., 12(2015), 4442-4449.
  • [6] Matkovic, A., Peˇcari´c, J. and Peri´c, I., A variant of Jensen’s inequality of Mercer’s type for operators with applications, Linear Algebra Appl., 418(2006), 551-564.
  • [7] Mercer, A. McD., A variant of Jensen’s inequality, JIPAM, 4(2003), Article 73.
  • [8] Niezgoda, M., A generalization of Mercer’s result on convex functions, Nonlinear Anal., 71(2009), 2771-2779.
  • [9] Pavic, Z., Convex function and its secant, Adv. Inequal. Appl., 2015(2015), Article 5.
  • [10] Pavic, Z., Generalizations of Jensen-Mercer’s inequality, J. Pure Appl. Math. Adv. Appl., 11(2014), 19-36.
  • [11] Pavic Z., Geometric and analytic connections of the Jensen and Hermite-Hadamard inequality, Math. Sci. Appl. E-Notes, 4(2016), 69-76.
  • [12] Pavic, Z., Inequalities with infinite convex combinations, submitted to FILOMAT.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Zlatko Pavic This is me

Publication Date April 30, 2019
Submission Date August 1, 2018
Published in Issue Year 2019

Cite

APA Pavic, Z. (2019). The Jensen-Mercer Inequality with Infinite Convex Combinations. Mathematical Sciences and Applications E-Notes, 7(1), 19-27. https://doi.org/10.36753/mathenot.559241
AMA Pavic Z. The Jensen-Mercer Inequality with Infinite Convex Combinations. Math. Sci. Appl. E-Notes. April 2019;7(1):19-27. doi:10.36753/mathenot.559241
Chicago Pavic, Zlatko. “The Jensen-Mercer Inequality With Infinite Convex Combinations”. Mathematical Sciences and Applications E-Notes 7, no. 1 (April 2019): 19-27. https://doi.org/10.36753/mathenot.559241.
EndNote Pavic Z (April 1, 2019) The Jensen-Mercer Inequality with Infinite Convex Combinations. Mathematical Sciences and Applications E-Notes 7 1 19–27.
IEEE Z. Pavic, “The Jensen-Mercer Inequality with Infinite Convex Combinations”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 19–27, 2019, doi: 10.36753/mathenot.559241.
ISNAD Pavic, Zlatko. “The Jensen-Mercer Inequality With Infinite Convex Combinations”. Mathematical Sciences and Applications E-Notes 7/1 (April 2019), 19-27. https://doi.org/10.36753/mathenot.559241.
JAMA Pavic Z. The Jensen-Mercer Inequality with Infinite Convex Combinations. Math. Sci. Appl. E-Notes. 2019;7:19–27.
MLA Pavic, Zlatko. “The Jensen-Mercer Inequality With Infinite Convex Combinations”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, 2019, pp. 19-27, doi:10.36753/mathenot.559241.
Vancouver Pavic Z. The Jensen-Mercer Inequality with Infinite Convex Combinations. Math. Sci. Appl. E-Notes. 2019;7(1):19-27.

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