Nuevas desigualdades tipo Jensen para funciones $\varphi$-convexas
Palabras clave:
$\varphi$-convex function, convex function, Green function, Jensen type inequalities. funciones $\varphi$-convexas, funciones convexas, funci\'on de Green, desigualdades del tipo Jensen.
Resumen
La desigualdad integral de Jensen tiene mucha importancia en cuanto a sus aplicaciones en diferentes campos de las matem\'aticas. En este art\'iculo encontramos una nueva desigualdad tipo Jensen para funciones cuya segunda derivada en valor absoluto es $\varphi$-convexa.
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Referencias
[1] Adil Khan M, Shahid Khan, Yu-Ming Chu. A new bound for the Jensen gap with applications in information theory. IEEE Access DOI 10.1109/ACCESS.2020.2997397, (2019).
[2] M. Adil Khan, M. Hanif, Z. A. Hameed Khan, K. Ahmad, and Y.-M. Chu. Association of Jensen?s ̃
[3] I. Burbea and C. R. Rao. On the convexity of some divergence measures based on entropy functions. IEEE Trans. Inform. Theory., vol. 28, pp. 489-495, (1982).
[4] S. S. Dragomir, M. Adil Khan, and A. Abathun. Refinement of the Jensen integral inequality. Open Math., vol. 14, pp. 221-228, (2016).
[5] L. HorvA¡th, D. Pecaric, and J. Pecaric. Estimations of f -and RA⃝c nyi divergences by using a cyclic
refinement of the Jensen?s inequality. Bull. Malays. Math. Sci. Soc., vol. 42, pp. 933?946, (2019).[6] M. E. Gordji, M. R. Delavar, and M. De La Sen, On φ-convex functions, J. Math. Inequal. 10, no 1, (2016) 173-183.
[7] Grinalatt M., Linnainmaa J. T. Jensen’s Inequality, parameter uncertainty and multiperiod investment, Review of Asset Pricing Studies. 1, (2011) 1-34.
[8] J. H. Justice (editor), Maximum Entropy and Bayesian Methods in Applied Statistics. Cambridge Uni- versity Press: Cambridge, (1986).
[9] S. Khan, M. Adil Khan, and Y.-M. Chu, Converses of the Jensen inequality derived from the Green functions with applications in information theory. Math. Method. Appl. Sci., vol. 43, pp. 2577-2587, (2020).
[10] Li X. F., Dong J. L. and Liu Q. H., Lipschitz B-vex functions and nonsmooth programming, J. Optimiz. Theory. App., 3, (1997) 557-573.
̃
[11] N. Latif, D. Pecaric, and J. Pecaric, Majorization, “useful” CsiszA¡r divergence and “useful” Zipf-
Mandelbrot law. Open Math., vol. 16, pp. 1357?1373, (2018).
[12] H. R. Moradi, M. E. Omidvar, M. Adil Khan, and K. Nikodem, Around Jensen’s inequality for strongly
convex functions. Aequat. Math., vol. 92, no. 1, pp. 25?37, (2018).
[13] Mangasarian O. L., Pseudo-Convex Functions, SIAM. J. Control. 3, (1965) 281-290.
[14] Mohan S. R. and Neogy S. K., On invex sets and preinvex functions, J. Math. Anal. Appl. 189, (1995) 901-908.
̈
[15] M. E. Ozdemir, C. Yildiz, A. O. Akdemir and E. Set, On some inequalities for s-convex functions and
applications, J. Inequal and Appl. 48, (2013) 1-11.
[16] D. Pecaric, J. Pecaric, and M. Rodic. About the sharpness of the Jensen inequality. J. Inequal. Appl.,
vol. 2018, p. Article ID 337, (2018).
[17] J.Pecaric,F.Proschan,andY.L.Tong,Convexfunctions,partialorderings,andstatisticalapplications, no. 187, Mathematics in Science and Engineering, Academic Press, Inc., Boston, MA (1992).
[18] Ruel J.J., Ayres M. P. Jensen’s inequality predicts effects of environmental variations, Trends in Eco- logy and Evolution. 14 (9), (1999) 361-366.
[19] Sarikaya M.Z., Filiz H., Kiris M. E. On some generalized integral inequalities for Riemann Lioville Fractional Integral, Filomat. 29:6, (2015) 1307-1314.
[20] Set E., New inequalities of Ostrowski type for mapping whose derivatives are s-convex in the second sense via fractional integrals, Comput.Math. Appl., 63, (2012) 1147-1154.
[21] S. Varosˆanec., On h-convexity, J. Math. Anal. Appl. 326, no. 1, 303311.MR2277784 (2007).
[22] VivasM.,Garc ́ıaC.,OstrowskiTypeinequalitiesforfunctionswhosederivativesare(m,h1,h2)-convex,
Appl. Math and Inf. Sci., 11, no 1, (2017) 79-86.
[23] Vivas M., Fe ́jer Type inequalities for (s, m)-convex functions in the second sense, Appl. Math and Inf. Scl., 10, no 5, (2016) 1689-1696.
[24] Rangel-Oliveros Y.C. and Vivas-Cortez M. J., On some Hermite-Hadamard type inequalities for fun- ˆ
ctions whose second derivative are convex generalized. Vol. V, NA◦2, (2018) 21-31.
[25] Rangel-Oliveros Y.C. and Vivas-Cortez M. J., Ostrowski type inequalities for functions whose se- cond derivative are convex generalized. Applied Mathematics and Information Sciences, Vol.12, No 6, (2018) 1055-1064.
[26] Vivas-Cortez, M., Abdeljawad, T., Mohammed, P.O., Rangel-Oliveros, Y. Simpson’s integral inequali- ties for twice differentiable convex functions. Math. Probl. Eng. 2020, Article ID 1936461 (2020)
[27] Vivas-Cortez M. and Rangel-Oliveros Y., An inequality related to s-φ-convex functions. Appl. Math. Inf. Sci., 14 (2020), 151-154.
[2] M. Adil Khan, M. Hanif, Z. A. Hameed Khan, K. Ahmad, and Y.-M. Chu. Association of Jensen?s ̃
[3] I. Burbea and C. R. Rao. On the convexity of some divergence measures based on entropy functions. IEEE Trans. Inform. Theory., vol. 28, pp. 489-495, (1982).
[4] S. S. Dragomir, M. Adil Khan, and A. Abathun. Refinement of the Jensen integral inequality. Open Math., vol. 14, pp. 221-228, (2016).
[5] L. HorvA¡th, D. Pecaric, and J. Pecaric. Estimations of f -and RA⃝c nyi divergences by using a cyclic
refinement of the Jensen?s inequality. Bull. Malays. Math. Sci. Soc., vol. 42, pp. 933?946, (2019).[6] M. E. Gordji, M. R. Delavar, and M. De La Sen, On φ-convex functions, J. Math. Inequal. 10, no 1, (2016) 173-183.
[7] Grinalatt M., Linnainmaa J. T. Jensen’s Inequality, parameter uncertainty and multiperiod investment, Review of Asset Pricing Studies. 1, (2011) 1-34.
[8] J. H. Justice (editor), Maximum Entropy and Bayesian Methods in Applied Statistics. Cambridge Uni- versity Press: Cambridge, (1986).
[9] S. Khan, M. Adil Khan, and Y.-M. Chu, Converses of the Jensen inequality derived from the Green functions with applications in information theory. Math. Method. Appl. Sci., vol. 43, pp. 2577-2587, (2020).
[10] Li X. F., Dong J. L. and Liu Q. H., Lipschitz B-vex functions and nonsmooth programming, J. Optimiz. Theory. App., 3, (1997) 557-573.
̃
[11] N. Latif, D. Pecaric, and J. Pecaric, Majorization, “useful” CsiszA¡r divergence and “useful” Zipf-
Mandelbrot law. Open Math., vol. 16, pp. 1357?1373, (2018).
[12] H. R. Moradi, M. E. Omidvar, M. Adil Khan, and K. Nikodem, Around Jensen’s inequality for strongly
convex functions. Aequat. Math., vol. 92, no. 1, pp. 25?37, (2018).
[13] Mangasarian O. L., Pseudo-Convex Functions, SIAM. J. Control. 3, (1965) 281-290.
[14] Mohan S. R. and Neogy S. K., On invex sets and preinvex functions, J. Math. Anal. Appl. 189, (1995) 901-908.
̈
[15] M. E. Ozdemir, C. Yildiz, A. O. Akdemir and E. Set, On some inequalities for s-convex functions and
applications, J. Inequal and Appl. 48, (2013) 1-11.
[16] D. Pecaric, J. Pecaric, and M. Rodic. About the sharpness of the Jensen inequality. J. Inequal. Appl.,
vol. 2018, p. Article ID 337, (2018).
[17] J.Pecaric,F.Proschan,andY.L.Tong,Convexfunctions,partialorderings,andstatisticalapplications, no. 187, Mathematics in Science and Engineering, Academic Press, Inc., Boston, MA (1992).
[18] Ruel J.J., Ayres M. P. Jensen’s inequality predicts effects of environmental variations, Trends in Eco- logy and Evolution. 14 (9), (1999) 361-366.
[19] Sarikaya M.Z., Filiz H., Kiris M. E. On some generalized integral inequalities for Riemann Lioville Fractional Integral, Filomat. 29:6, (2015) 1307-1314.
[20] Set E., New inequalities of Ostrowski type for mapping whose derivatives are s-convex in the second sense via fractional integrals, Comput.Math. Appl., 63, (2012) 1147-1154.
[21] S. Varosˆanec., On h-convexity, J. Math. Anal. Appl. 326, no. 1, 303311.MR2277784 (2007).
[22] VivasM.,Garc ́ıaC.,OstrowskiTypeinequalitiesforfunctionswhosederivativesare(m,h1,h2)-convex,
Appl. Math and Inf. Sci., 11, no 1, (2017) 79-86.
[23] Vivas M., Fe ́jer Type inequalities for (s, m)-convex functions in the second sense, Appl. Math and Inf. Scl., 10, no 5, (2016) 1689-1696.
[24] Rangel-Oliveros Y.C. and Vivas-Cortez M. J., On some Hermite-Hadamard type inequalities for fun- ˆ
ctions whose second derivative are convex generalized. Vol. V, NA◦2, (2018) 21-31.
[25] Rangel-Oliveros Y.C. and Vivas-Cortez M. J., Ostrowski type inequalities for functions whose se- cond derivative are convex generalized. Applied Mathematics and Information Sciences, Vol.12, No 6, (2018) 1055-1064.
[26] Vivas-Cortez, M., Abdeljawad, T., Mohammed, P.O., Rangel-Oliveros, Y. Simpson’s integral inequali- ties for twice differentiable convex functions. Math. Probl. Eng. 2020, Article ID 1936461 (2020)
[27] Vivas-Cortez M. and Rangel-Oliveros Y., An inequality related to s-φ-convex functions. Appl. Math. Inf. Sci., 14 (2020), 151-154.
Publicado
2020-12-30
Cómo citar
Rangel-Oliveros, Y., & Vivas-Cortez, M. (2020). Nuevas desigualdades tipo Jensen para funciones $\varphi$-convexas. Revista MATUA ISSN: 2389-7422, 7(1), 36-43. Recuperado a partir de https://investigaciones.uniatlantico.edu.co/revistas/index.php/MATUA/article/view/2775
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