Aydin, IsmailAkgun, Ramazan2026-04-252026-04-2520262035-6803https://hdl.handle.net/11486/8644We give some new embeddings results for weighted grand Lebesgue spaces L-omega(p)),delta (Omega), where Omega subset of R-d is a open bounded subset. We also obtain the boundedness of the Kantorovich operator K-n in L-omega(p),delta) [0, 1]. In addition, we establish two direct estimates by K-functionals of the rate of approximation in L-omega(p),delta) [0,1].We generalize the direct estimate inequality in classical Lebesgue spaces L-p [0,1] to L-omega(p),delta)[0,1] using the boundedness of the Hardy-Littlewood maximal operator in L-omega(p),delta) [0,1]. Finally, we obtain similar results in [8] for the spaces L-omega(p),delta) [0,1].eninfo:eu-repo/semantics/closedAccessArticle1912182-s2.0-105034302991N/AWOS:001728284900001Q1