NEW FRACTAL SIMPSON ESTIMATES FOR TWICE LOCAL DIFFERENTIABLE GENERALIZED CONVEX MAPPINGS

Butt S. I., Inam H., Dokuyucu M. A.

Applied and Computational Mathematics, cilt.23, sa.4, ss.474-503, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.30546/1683-6154.23.4.2024.474
  • Dergi Adı: Applied and Computational Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.474-503
  • Anahtar Kelimeler: Fractal Sets, Fractional Opera-tors, Generalized Convexity, Hölder-Yang’s-Inequality, Simpson Type Inequalities
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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.