Enhancement of the Cauchy-Schwarz inequality and its implications for numerical radius inequalities
作者：R. Nayak · 发表于：Filomat · 年份：2025 · DOI：10.2298/fil2530679y
In this article, we establish an improvement of the Cauchy-Schwarz inequality. Let x, y ∈ H, and let f: (0, 1) → \mathbb{R} ^{+} > be a well-defined function, where <![CDATA[ \mathbb{R} > ^{+} > denote the set of all positive real numbers. Then | ⟨x, y ⟩2|≤ f(t)/1+f(t)∥x2∥∥y2∥+1/1 +f(t) |⟨x , y ⟩|∥x ∥ ∥ y∥. We have applied this result to derive new and improved upper bounds for the numerical radius. 2025 10595 10607 http://creativecommons.org/publicdomain/zero/1.0/ 10.2298/FIL2530595N https://doiserbia.nb.rs/Article.aspx?ID=0354-51802530595N M. Al-Dolat, I. Jaradat, A refinement of the Cauchy-Schwarz inequality accompanied by new numerical radius upper bounds, Filomat, 37 (2023), no. 3, 971-977. M. W Alomari, On Cauchy–Schwarz type inequalities and applications to numerical radius inequalities, Ricerche di Matem- atica, (2022), DOI: 10.1007/s11587-022-00689-2. N. Altwaijry, S. S. Dragomir, K. Feki, Upper bounds for the Euclidean spectral radius of operators via joint norms, Linear Multilinear Algebra 72 (2024), no. 5, 875-890. J. S. Aujla, F. C. Silva, Weak majorization inequalities and convex functions, Linear Algebra Appl. 369 (2003), 217–233. W. Bani-Domi, F. Kittaneh, Refined and generalized numerical radius inequalities for 2 × 2 operator matrices, Linear Algebra Appl. 624 (2021), 364–386. P. Bhunia, Improved bounds for the numer...