Some inequalities for a new class of convex functions with applications via local fractional integral
type: Item
instance of: scholarly article
title: Some inequalities for a new class of convex functions with applications via local fractional integral
zbMATH Open document ID: 1464.26020
DOI: 10.1155/2021/6663971
author: Hu Ge-JiLe
author: Saima Rashid
author: Fozia Bashir Farooq
author: Sobia Sultana
published in: Journal of Function Spaces
publication date: 2021-05-17T00:00:00Z
review text: Summary: The understanding of inequalities in convexity is crucial for studying local fractional calculus efficiency in many applied sciences. In the present work, we propose a new class of harmonically convex functions, namely, generalized harmonically \(\psi\)-\(s\)-convex functions based on fractal set technique for establishing inequalities of Hermite-Hadamard type and certain related variants with respect to the Raina's function. With the aid of an auxiliary identity correlated with Raina's function, by generalized Hölder inequality and generalized power mean, generalized midpoint type, Ostrowski type, and trapezoid type inequalities via local fractional integral for generalized harmonically \(\psi\)-\(s\)-convex functions are apprehended. The proposed technique provides the results by giving some special values for the parameters or imposing restrictive assumptions and is completely feasible for recapturing the existing results in the relative literature. To determine the computational efficiency of offered scheme, some numerical applications are discussed. The results of the scheme show that the approach is straightforward to apply and computationally very user-friendly and accurate.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 7348604
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6663971
OpenAlex ID: W3142469695
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description: scientific article; zbMATH DE number 7348604