On Generalized Harmonically ψ-MT-Convex Functions via Local Fractional Integrals and some Applications

Authors

Miguel Vivas-Cortez, Escuela de Ciencias F ́ısicas y Matema ́ticas, Facultad de Ciencias Naturales y Exactas, Pontificia Universidad Cato ́lica del Ecuador, Sede Quito, EcuadorFollow
Muhammad Shoaib Saleem, Department of Mathematics, University of Okara, PakistanFollow
Ahsan Fareed Shah, Department of Mathematics, University of Okara, Pakistan\\ Department of Mathematics, Government College University Lahore, Pakistan\\ Quaid E Azam Academy for Educational Development, Lahore, PakistanFollow
Waqas Nazeer, Department of Mathematics, Government College University Lahore, PakistanFollow
Jorge Eliecer Herna ́ndez Herna ́ndez, Departamento de Te ́cnicas Cuantitativas, Decanato de Ciencias Econo ́micas y Empresariales, Universidad Centroccidental Lisandro Alvarado, Barquisimeto, VenezuelaFollow

Author Country (or Countries)

Ecuador

Abstract

In this work, we introduce a new class of harmonically convex functions, namely, generalized harmonically ψ-MT-convex functions established on fractal set techniques, for establishing inequalities of Hermite-Hadamard type and certain related variants with respect to the Raina’s function. With the help of an auxiliary identity associated with Raina’s function, by generalized Holder inequality and generalized power mean, generalized midpoint type, Ostrowski type, and trapezoid type inequalities via local fractional integral for generalized harmonically ψ-MT-convex functions are given. The introduced technique gives the results by establishing some special values for the parameters or applying restrictive suppositions and is entirely practicable for regaining the existing inequalities in the related literature.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/170303

Recommended Citation

Vivas-Cortez, Miguel; Shoaib Saleem, Muhammad; Fareed Shah, Ahsan; Nazeer, Waqas; and Eliecer Herna ́ndez Herna ́ndez, Jorge (2023) "On Generalized Harmonically ψ-MT-Convex Functions via Local Fractional Integrals and some Applications," Applied Mathematics & Information Sciences: Vol. 17: Iss. 3, Article 3.
DOI: http://dx.doi.org/10.18576/amis/170303
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss3/3