10 papers
Generalizations of Chainability and Compactness, and the Hypertopologies
Ajit Kumar Gupta, Saikat Mukherjee
We study two properties for subsets of a metric space. One of them is generalization of chainability, finite chainability, and Menger convexity for metric spaces; while the other i…
Lebesgue Number and Total Boundedness
Ajit Kumar Gupta, Saikat Mukherjee
A generalization of the Lebesgue number lemma is obtained. It is proved that, if each countably infinite locally finite open cover of a chainable metric space has a Lebesgue nu…
Induced Homeomorphism and Atsuji Hyperspaces
Ajit Kumar Gupta, Saikat Mukherjee
Given uniformly homeomorphic metric spaces and , it is proved that the hyperspaces and are uniformly homeomorphic, where denotes the collection of all n…
On wovenness of K-fusion frames
Animesh Bhandari, Saikat Mukherjee
In frame theory literature, there are several generalizations of frame, K-fusion frame presents a flavour of one such generalization, basically it is an intertwined replica of K-fr…
Menger Convexity and Fixed Point Results
Ajit Kumar Gupta, Saikat Mukherjee
Shimizu and Takahashi proved that every decreasing sequence of nonempty, bounded, closed, convex subsets of a complete, uniformly Takahashi convex metric space has nonempty interse…
On Nonempty Intersection Properties in Metric Spaces
Ajit K. Gupta, Saikat Mukherjee
The classical Cantor's intersection theorem states that in a complete metric space , intersection of every decreasing sequence of nonempty closed bounded subsets, with diameter…
Characterizations of Weaving K-frames
Animesh Bhandari, Debajit Borah, Saikat Mukherjee
In distributed signal processing frames play significant role as redundant building blocks. Bemrose et. al. were motivated from this concept, as a result they introduced weaving fr…
Characterizations of woven frames
Animesh Bhandari, Saikat Mukherjee
In a separable Hilbert space , two frames and are said to be woven if there are constants so that for every $σ\subs…
Perturbations on K-fusion frames
Animesh Bhandari, Saikat Mukherjee
K-fusion frames are generalizations of fusion frames in frame theory. This article characterizes various kinds of property of K-fusion frames. Several perturbation results on K-fus…
Atomic subspaces for operators
Animesh Bhandari, Saikat Mukherjee
This paper introduces the concept of atomic subspaces with respect to a bounded linear operator. Atomic subspaces generalize fusion frames and this generalization leads to the noti…