In diverse branches of mathematics, several inequalities have been studied and applied. this article, we improve Furuta’s inequality. Subsequently, apply improvement to obtain new radius that not reported in the current literature. Numerical examples illustrate main findings.

This article is devoted to studying some new numerical radius inequalities for Hilbert space operators. Our analysis enables us improve an earlier bound due Kittaneh. It shown, among other, that if $A\in \mathcal{B}(\mathcal{H})$, then \[ \frac{1}{8}\left( {{\left\| A+{{A}^{*}} \right\|}^{2}}+{{\left\| A-{{A}^{*}} \right\|}^{2}} \right)\le \omega ^{2}\left( A \right) \le \left\| \frac{{{\left| ...

The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which generalizations Hilbert spaces. We demonstrate how these can be employed derive novel A-numerical radius inequalities, where A denotes a positive semidefinite operator complex space. Some our expand upon the existing literature on numerical with space operators, import...

in this paper, direct numerical simulation of two-phase incompressible gas-liquid flow for simulation of bubble motion in a microtube is presented. microtube radius is 10 µm. the interface is tracked using volume of fluid (vof) method with continuous surface force (csf) model. the flow is solved using a finite volume scheme, based on piso algorithm. numerical simulation is performed on a axisym...

In this paper, we prove that each of the following functions is convex on R: f(t) = wN(AtXA1?t ? A1?tXAt), g(t) wN(AtXA1?t), and h(t) wN(AtXAt) where A > 0, X Mn N(.) a unitarily invariant norm onMn. Consequently, answer positively question concerning convexity function t w(AtXAt) proposed by in (2018). We provide some generalizations extensions wN(.) using Kwong functions. More precisely, w...

Let $$\mathcal {H}$$ be a complex Hilbert space with inner product $$\langle \cdot , \rangle $$ and let A non-zero bounded positive linear operator on {H}.$$ $$\mathbb {B}_A(\mathcal {H})$$ denote the algebra of all operators which admit A-adjoint, $$N_A(\cdot )$$ seminorm . The generalized A-numerical radius $$T\in \mathbb is defined as $$\begin{aligned} \omega _{N_A}(T)=\displaystyle {\sup _{...