Some integral inequalities involving the k-Beta function and generalized convex stochastic processes.

• Hernández H, Jorge Eliecer ^[1]
  1. [1] Universidad Centroccidenta Lisandro Alvarado
• Localización: MATUA: Revista de matemática de la universidad del Atlántico, ISSN-e 2389-7422, Vol. 6, Nº. 1, 2019 (Ejemplar dedicado a: Revista MATUA Vol. 6 No. 1.), págs. 2-16
• Idioma: inglés
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• Resumen

  • In the present work some integral inequalities that involve the k-Beta function and stochastic processes whose absolute values posses the property of convexity, or P-convexity, s-convexity in the second sense or (m; h1; h2)-convexity are established. Similarly, some others integral inequalities for stochastic processes whose r-th powers of its absolute values posses these kind of generalized convexity are established making use of the Hölder’s inequality and power mean inequality.

• Referencias bibliográficas
  • M. Alomari , M. Darus. On The Hadamard’s Inequality for Log-Convex Functions on the Coordinates. J. Ineq. Appl., 2009, Article ID 283147,...
  • M. Alomari, M. Darus, S.S. Dragomir, P. Cerone . Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense....
  • A. Bain, P. Crisan. Fundamentals of Stochastic Filtering. Stochastic Modelling and Applied Probability, 60. Springer, New York. 2009.
  • J. C. CortÉs , L. Jódar, L. Villafuerte. Numerical solution of random dierential equations: A mean square approach. Mathematical and Computer...
  • P. Devolder, J. Janssen, R. Manca. Basic stochastic processes. Mathematics and Statistics Series, ISTE, London; John Wiley and Sons, Inc....
  • R. Diaz, E. Pariguan. On hypergeometric functions and Pochhammer k-symbol. Divulgaciones Matemáticas, 15 , No. 2, 179-192, (2007).
  • J. E. Hernández Hernández, J.F. Gómez. Hermite-Hadamard type inequalities, convex stochastic processes and Katugampola fractional integral....
  • (2018). https://doi.org/10.18273/revint.v36n2-2018005.
  • J. E. Hern´andez Hern´andez, J.F. G´omez . Hermite Hadamard type inequalities for Stochastic Processes whose Second Derivatives are (m; h1;...
  • D. Kotrys. Hermite-Hadamard inequality for convex stochastic processes. Aequationes Mathematicae, 83, 143-151, (2012). https://doi.org/10.1007/s00010-011-0090-1
  • D. Kotrys. Remarks on strongly convex stochastic processes. Aequat. Math., 86 , 91-98, (2013). https://doi.org/10.1007/s00010-012-0163-9
  • T. Mikosch. Elementary stochastic calculus with finance in view. Advanced Series on Statistical Science and Applied Probability, World Scientific...
  • B. Nagy. On a generalization of the Cauchy equation. Aequationes Math., 11 , 165-171, (1974)
  • K. Nikodem. On convex stochastic processes. Aequationes Math., 20, No. 1, 184-197, (1980).
  • Z. Pavi´c, M. Avci Ardic. The most important inequalities for m-convex functions, Turk J. Math., 41, 625-635, (2017). https://doi.org/10.3906/mat-1604-45
  • A. Rehman, S. Mubeen, R. Safdar, N. Sadiq. Properties of k-Beta function with several variables, Open Math., 13 , 308-320, (2015). https://doi.org/10.1515/math-2015-0030
  • E. Set, M. Tomar, S. Maden. Hermite Hadamard Type Inequalities for s-Convex Stochastic Processes in the Second Sense, Turkish Journal of Analysis...
  • E. Set, A. Akdemir, N. Uygun. On New Simpson Type Inequalities for Generalized Quasi-Convex Mappings, Xth International Statistics Days Conference,...
  • M. Shaked, J. Shantikumar. Stochastic Convexity and its Applications, Arizona Univ. Tuncson. 1985.
  • J.J. Shynk. Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications, Wiley, 2013
  • A. Skowronski. On some properties of J-convex stochastic processes, Aequationes Mathematicae, 44, 249-258, (1992)
  • A. Skowronski. On Wright-Convex Stochastic Processes. Ann. Math. Sil., 9 , 29-32, (1995)
  • K. Sobczyk . Stochastic differential equations with applications to physics and engineering, Kluwer Academic Publishers B.V.,1991.
  • M. Tomar, E. Set, S. Maden. Hermite-Hadamard Type Inequalities For Log-Convex Stochastic Processes, J. New Theory, 2015, No. 2, 23-32, (2015)
  • M.J. Vivas-Cortez , Y.C Rangel Oliveros. Ostrowski Type Inequalities for Functions Whose Second Derivatives are Convex Generalized, App. Math....