Akademik Veri Yönetim Sistemi
Indian Journal of Mathematics, cilt.66, sa.2, ss.229-255, 2024 (Scopus)
To tackle the challenges posed by natural problems, integral calculation becomes imperative. When direct integration falls short, approximating the integral becomes necessary, employing quadrature formulas like Newton-Cotes or Gauss methods. This study delves into various approximations for the left side of the generalized Gauss-Jacobi quadrature formula, drawing insights from prior research and existing literature. The results obtained rely on a specific identity and on the notion of r-convexity. Multiple techniques are employed to break down integrals, including the use of Hölder and Minkowski inequalities, as well as linearization methods like the Young and Bernoulli inequalities.