Akshay S. Rane

collaborators

3 papers

math.GM2021

Zabreiko's lemma in 2-normed space and its applications

Akshay S. Rane

We prove the Zabreiko's lemma in 2-Banach spaces. As an application we shall prove a version of the closed graph theorem and open mapping theorem.

math.FA2021

A note on the 2-dual space of $L^{p} [0, 1]$

Akshay S. Rane

In the present note, we are interested in bounded 2-functionals and 2-dual spaces of $L^{p} [0, 1]$ . The 2-dual spaces of the sequence space $l^{p}$ is considered in the literature. But…

math.NA2020

Richardson extrapolation for the iterated Galerkin solution of Urysohn integral equations with Green's kernels

Gobinda Rakshit, Akshay S. Rane, Kshitij Patil

We consider a Urysohn integral operator $K$ with kernel of the type of Green's function. For $r \geq 1$ , a space of piecewise polynomials of degree $\leq r - 1$ with respe…

Zabreiko's lemma in 2-normed space and its applications

A note on the 2-dual space of Lp[0,1]

Richardson extrapolation for the iterated Galerkin solution of Urysohn integral equations with Green's kernels

A note on the 2-dual space of $L^{p} [0, 1]$