Una Variante de la desigualdad de Jensen-Mercer para funciones $h-$convexas y funciones de operadores $h-$convexas.

• Vivas Cortez, Miguel Jose ^[1] ; Hernández Hernández, Jorge Eliecer ^[2]
  1. [1] Pontificia Universidad Católica del Ecuador

     Pontificia Universidad Católica del Ecuador

     Quito, Ecuador

     
  2. [2] Universidad Centroccidental Lisandro Alvarado

     Universidad Centroccidental Lisandro Alvarado

     Venezuela

     
• Localización: MATUA: Revista de matemática de la universidad del Atlántico, ISSN-e 2389-7422, Vol. 4, Nº. 2, 2017 (Ejemplar dedicado a: Revista MATUA), págs. 62-76
• Idioma: español
• Títulos paralelos:
  • A variant of Jensen-Mercer Inequality for $h-$convex functions and Operator $h-$convex functions.
• Enlaces
  • Texto completo
• Resumen
  • español

    En este art\'{i}culo encontramos nuevas desigualdades relacionadas con la bien conocida desigualdad de Jensen-Mercer, y correspondientes aplicaciones a la Teoría de Operadores, usando funciones $h-$convexas y funciones de operadores $h-$convexas. Los resultados encontrados generalizan otros previamente formulados.

  • English

    In the present paper, we have find some new inequalities related to the wellknown Jensen-Mercer Inequality, and its corresponding application to thetheory of Operators, using $h-$convex functions and operator $h-$convexfunctions. These results generalize some others found in previous investigations.

• Referencias bibliográficas
  • [1] J.L. Aujla, H. L. Vasudeva,Convex and monotone operator functions, Annales Polonici Mathematici62 (1995) 1–11.
  • [2] V. Bacak., R. Turkmen,New Inequalities for operator convex functions, Journal of Inequalities andApplications 2013 (2013): 190.
  • [3] H.H. Bauschke, P.L. Combettes,Convex Analysis and Monotone Operator Theory in Hilbert Spaces,Springer New York Dordrecht Heidelberg London,...
  • [4] W.W. Breckner,Stetigkeitsaussagen f ̈ur eine Klasse verallgemeinerter konvexer funktionen in topolo-gischen linearen R ̈aumen, Pub....
  • [5] J. Bendat and S. Sherman,Monotone and Convex Operator Functions, Trans. Amer. Math. Soc. 79(1955) 58–71
  • [6] L. Bougoffa.New Inequalities for convex functions. Journal of Inequalities in Pure and Applied Mat-hematics. Vol,/(4), Nro. 148. 2006
  • [7] P. Chansangiam.A Survey on Operator Monotonicity, Operator convexity and Operator Means.Inter-national Journal of Analysis. Vol. 2015....
  • [8] M.J. Cloud, B.C. Drachman.Inequalities: With Applications to Engineering. Springer-Verlag, NewYork, Inc. 1998
  • [9] S.S. Dragomir.Hermite Hadamard’s type inequalities for operator convex functions. Journal of Mat-hematical Inequalities. 4(4), 2010,...
  • [10] S.S. Dragomir, J. Peˇcari ́c, L.E Persson.Some inequalities of Hadamard type. Soochow J. Math.21(1995) 335 – 341
  • [11] U. Franz, F. Hial, E. Ricard.Higher Order Exyension of L ̈owner’s Theory: Operator k-Tone Functions,arXiv: 1105.3881v4. 201474
  • [12] A.G. Ghazanfari.The Hermite Hadamard type inequalities for operator s-convex functions. Journal ofAdvanced Research in Pure Mathematics....
  • [13] E.Godunova, V. Levin.Neravenstva dlja funkcii ̆sirokogo klassa, soder ̆za ̆s ̆cego vypuklye, monotonnye,inekotorye drugie vidy funkcii,...
  • [14] J.S Hadamard.Etude sur les propi`et ́es des fonctions entieres et en particulier d ́une fontion considererper Riemann, J. Math....
  • [15] F. Hansen and J.K. Pedersen.Jensen’s Inequality for Operators and L ̈oowner Theorem, Math. Ann.258 (1982), pp 229-241
  • [16] G.H. Hardy, J.E. Littlewood, G. Polya.Inequalities.Cambidge University Press. London. 1934
  • [17] ̇I. Is ̧can,Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, Stud.Univ. Babes ̧ Bolyai Math. 60(2015)...
  • [18] I. Is ̧can, M. Kunt,Hermite-Hadamard-Fej ́er type inequalities for quasi-geometrically convex functionsvia fractional integrals, Hindawi...
  • [19] J.L.W Jensen,Sur les fonctions convexes et le inequaliti ́es entre les valeurs moyennes, Acta Math.32(1906) 175 – 193.
  • [20] A. R. Khan, J. Peˇcari ́c, M. Praljak,A Note on Generalized Mercer’s, Bulletin of the Malaysian Mathe-matical Sciences Society 40 (2017)...
  • [21] A. Kor`anyi,On a Theorem of L ̈owner and its Connection with of Resolvent of Transformation, ActaSci. Math. (Szeged) 17 (1956)...
  • [22] P. Kraus, ̈Uber Konvexe Matrixfunktionen, Math. Z. 41 (1936) 18–42.
  • [23] K. L ̈owner, ̈Uber Monotone Matrixfunktionen, Math. Z. 38 (1934) 177–216.
  • [24] A. Matkovi ́c, J. Peˇcari ́c, I. Peri ́c,A variant of Jensen’s inequality of Mercer’s type for operators withapplications, Linear Algebra...
  • [25] A. McD. Mercer,A variant of Jensen’s inequality, J. Inequal. Pure Appl. Math. 4 (2003) Article 73
  • [26] M. Minculete, F.C. Mitroi,F ́ejer-type inequalitiesAust. J. Math. Anal. Appl. 9 (2012) 8 pp.
  • [27] M. Kian, M.S. Moslehian,Refinements of the operator Jensen-Mercer inequality, Electron, J. LinearAlgebra 26 (2013) 742–753.
  • [28] M. Niezgoda,A generalization of Mercer’s result on convex functions, Nonlinear Analysis 71 (2009)2771-2779.
  • [29] J. Park,Inequalities of Hermite-Hadamard-Fej ́er type for convex functions via fractional integrals,International Journal...
  • [30] A. Taghavi, V. Darvish, M. Nazari, S.S. Dragomir,Some Inequalities Associated with the Hemite-Hadamard Inequalities for...
  • [31] S. Varo ̆sanec,On h convexity, J. Math. Anal. Appl. 326 (2007) 303 – 311
  • [32] X. Zhan,Matrix Inequalities, Lectures Notes in Mathematics, Springer-Verlag Berlin Heidelberg, 2002.