TY - JOUR
T1 - On Generalized Harmonically Ψ-MT-Convex Functions via Local Fractional Integrals and some Applications
AU - Vivas-Cortez, Miguel
AU - Saleem, Muhammad Shoaib
AU - Shah, Ahsan Fareed
AU - Nazeer, Waqas
AU - Hernandez, Jorge Eliecer Hernandez
N1 - Publisher Copyright:
© 2023 NSP Natural Sciences Publishing Cor.
PY - 2023/5/1
Y1 - 2023/5/1
N2 - 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.
AB - 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.
KW - Fractal set
KW - Generalized Harmonically Ψ-MTconvex function
KW - Harmonically-convex function
KW - Hermite Hadamard type inequality and Local fractional integral
KW - MT Convex function
KW - Raina‘s function
UR - http://www.scopus.com/inward/record.url?scp=85153781445&partnerID=8YFLogxK
U2 - 10.18576/amis/170303
DO - 10.18576/amis/170303
M3 - Article
AN - SCOPUS:85153781445
SN - 1935-0090
VL - 17
SP - 417
EP - 429
JO - Applied Mathematics and Information Sciences
JF - Applied Mathematics and Information Sciences
IS - 3
ER -