Hermite-Hadamard Type Mean Square Integral Inequalities for Stochastic Processes whose Twice Mean Square Derivative are Generalized η−convex.

Authors

Miguel Vivas-Cortez, Escuela de Ciencias F ́ısicas y Matema ́ticas , Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cato ́lica del Ecuador, Av. 12 de Octubre 1076. Apartado, Quito 17-01-2184, EcuadorFollow
Artion Kashuri, Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, L. Pavaresia, Vlora 1001, Vlore, AlbaniaFollow
Carlos Garc ́ıa, Departamento de Matema ́ticas, Decanato de Ciencias y Tecnolog ́ıa, Universidad Centroccidental Lisandro Alvarado, Barquisimeto, VenezuelaFollow
Jorge E. Herna ́ndez Herna ́ndez, Departamento de Te ́cnicas Cuantitativas, Decanato de Ciencias Econo ́micas y Empresariales, Universidad Centroccidental Lisandro Alvarado, Av. Moran esq. Av. 20, Edf. Los Militares, Ofc.2, ZP: 3001,Matema ́ticas, Decanato de Ciencias y Tecnolog ́ıa, Universidad Centroccidental Lisandro Alvarado, Barquisimeto, VenezuelaFollow

Author Country (or Countries)

Ecuador

Abstract

In the present work, a new concept of generalized convexity (i.e. generalized η−convexity ) is established and applied to stochastic process.Using the aforementioned concept, some new Hermite - Hadamard type inequalities for stochastic processes are found. From these results, some other inequalities for convex stochastic processes and s-convex stochastic processes in the first sense are deduced. Some Lemmas are introduced and the classical Ho ̈lder and power mean inequalities are used as tools for the development of the main results.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140317

Recommended Citation

Vivas-Cortez, Miguel; Kashuri, Artion; Garc ́ıa, Carlos; and E. Herna ́ndez Herna ́ndez, Jorge (2020) "Hermite-Hadamard Type Mean Square Integral Inequalities for Stochastic Processes whose Twice Mean Square Derivative are Generalized η−convex.," Applied Mathematics & Information Sciences: Vol. 14: Iss. 3, Article 17.
DOI: http://dx.doi.org/10.18576/amis/140317
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss3/17