arXiv subjects
Publications and source records attributed to Lakshmi Narayan Mishra.
We define weighted mean summability method of double sequences in intuitionistic fuzzy normed spaces($IFNS$), and obtain necessary and sufficient Tauberian conditions under which convergence of double sequences in $IFNS$ follows from their weighted mean summability. This study reveals also Tauberian results for some known summation methods in the special cases.
In this paper, we prove the pointwise convergence and the rate of pointwise convergence for a family of singular integral operators in two-dimensional setting in the following form: \begin{equation*} L_{λ}\left( f;x,y\right) =\underset{D}{\iint }f\left( t,s\right) K_{λ}\left( t-x,s-y\right) dsdt,\text{ }\left( x,y\right) \in D, \end{equation*} where $D=\left \langle a,b\right \rangle \times \left \langle c,d\right \rangle $ is an arbitrary closed, semi-closed or open rectangle in $\mathbb{R}^{2}$ and $% λ\in Λ,$ $Λ$ is a set of non-negative indices with accumulation point $λ_{0}$. Also, we provide an example to support these theoretical results. In contrast to previous works, the kernel function $K_{λ}\left( t,s\right) $ does not have to be even, positive or 2$π-$periodic.
In the present paper, we consider Stancu type generalization of Baskakov-Szász operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function are also established for operators.