Hermite-hadamard type mean square integral inequalities for stochastic processes whose twice mean square derivative are generalized η-convex.

Miguel Vivas-Cortez; Artion Kashuri; Carlos García; Jorge E.Hernández Hernández

doi:10.18576/AMIS/140317

Hermite-hadamard type mean square integral inequalities for stochastic processes whose twice mean square derivative are generalized η-convex.

Miguel Vivas-Cortez^*, Artion Kashuri, Carlos García, Jorge E.Hernández Hernández

^*Corresponding author for this work

Faculty of Exact and Natural Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 Holder and power mean inequalities are used as tools for the development of the main results.

Original language	English
Pages (from-to)	493-502
Number of pages	10
Journal	Applied Mathematics and Information Sciences
Volume	14
Issue number	3
DOIs	https://doi.org/10.18576/AMIS/140317
State	Published - 1 May 2020

Bibliographical note

Publisher Copyright:
© 2020 NSP.

Funding

Miguel Vivas-Cortez is strongly grateful to Dirección de Investigación from Pontificia Universidad Católica del Ecuador for the technical support offered to the research project entitled: "Algunas desigualdades integrales para funciones convexas generalizadas y aplicaciones". Jorge E. Hernández Hernández would like thank to the Consejo de Desarrollo Científico, Humanístico y Tecnológico (CDCHT) from Universidad Centroccidental Lisandro Alvarado (Venezuela) also for the technical support that developed of this article.

Funders	Funder number
CDCHT
Universidad Centroccidental Lisandro Alvarado
Consejo de Desarrollo Científico, Humanístico, Tecnológico y de las Artes, Universidad de Los Andes Venezuela

Keywords

Generalized η-convex stochastic processes
Hermite-hadamard inequality
Mean square integral inequalities

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10.18576/AMIS/140317

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title = "Hermite-hadamard type mean square integral inequalities for stochastic processes whose twice mean square derivative are generalized η-convex.",

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 Holder and power mean inequalities are used as tools for the development of the main results.",

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author = "Miguel Vivas-Cortez and Artion Kashuri and Carlos Garc{\'i}a and Hern{\'a}ndez, {Jorge E.Hern{\'a}ndez}",

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AU - Vivas-Cortez, Miguel

AU - Kashuri, Artion

AU - García, Carlos

AU - Hernández, Jorge E.Hernández

PY - 2020/5/1

Y1 - 2020/5/1

N2 - 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 Holder and power mean inequalities are used as tools for the development of the main results.

AB - 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 Holder and power mean inequalities are used as tools for the development of the main results.

KW - Generalized η-convex stochastic processes

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ER -

Hermite-hadamard type mean square integral inequalities for stochastic processes whose twice mean square derivative are generalized η-convex.

Abstract

Bibliographical note

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Keywords

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