NEW FRACTAL SIMPSON ESTIMATES FOR TWICE LOCAL DIFFERENTIABLE GENERALIZED CONVEX MAPPINGS
Applied and Computational Mathematics, vol.23, no.4, pp.474-503, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 23 Issue: 4
- Publication Date: 2024
- Doi Number: 10.30546/1683-6154.23.4.2024.474
- Journal Name: Applied and Computational Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
- Page Numbers: pp.474-503
- Keywords: Fractal Sets, Fractional Opera-tors, Generalized Convexity, Hölder-Yang’s-Inequality, Simpson Type Inequalities
- Ondokuz Mayıs University Affiliated: Yes
Abstract
The main focus of this research is to provide a new auxiliary results of the Simpson’s notation for a local fractional function that is twice differentiable via extended-fractal integral operator. Using Hölder-Yang’s and Power-mean integral inequalities in conjunction with generalized convexity, we produce a series of new fractal Simpson’s error estimates. Additionally, we will use improved Yang’s inequalities to create new boundaries. Visual illustrations demon-strate the accuracy and supremacy of the offered technique. Applications to the c-type special, moment of random variables as well as wave-equations are given. In this work, we present an extension of previously published results.