An Extension of Left Radau Type Inequalities to Fractal Spaces and Applications
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Date
2024-09-23
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Abstract
In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for functions whose first-order local fractional derivatives are generalized convex and concave. The obtained results not only represent an extension of certain previously established findings to fractal sets but also a refinement of these when the fractal dimension µ is equal to one. Finally, to support our findings, we present a practical application to demonstrate the effectiveness of our results.
Description
2024, 13, 653
https://doi.org/10.3390/axioms13090653
Keywords
local fractional integrals, generalized convex functions, Gaussian quadrature, two-point left Radau rule, generalized Hölder inequality, improved generalized power mean inequality