This note is prepared based on the article titled “Linear Sketching over F2”(ECCC TR16-174) by Sampath Kannan, Elchanan Mossel and Grigory Yaroslavtsev. We quantitatively improve the parameters of Theorem 1.4 of the above work, as well as an earlier bound of ours. In particular, our result implies that for every ∈ (0, 12 ) and every constant δ > 0, the one-way communication complexity of any Bo...

Macrolide antibiotics are thought to clog up the ribosomal tunnel and thereby block general protein synthesis. By using a combination of elegant in vivo and in vitro approaches, Kannan et al. show that the inhibitory action of these drugs on bacterial protein synthesis is selective rather than global.

In this paper we present some best proximity point theorems for a combination of weak Kannan and Chatterjea nonlinear cyclic contraction and the MT functions in the frameworks of a metric space (X, d), thereby furnishing an optimal approximate solution to the equations of the form Tx = x, where T is a non-self mapping.

In this paper, we establish some common fixed point theorems for fuzzy mappings satisfying fuzzy contractive conditions which are general than Chatterjee type and Kannan type fuzzy contractive conditions on closed balls in a complete metric space. Our results generalize the corresponding results in the current literature. AMS (2000) subject classification: 45S40 • 47H10 • 54H25

We extend some known fixed point results for mappings satisfying Kannan type conditions to the context of K-metric spaces. Firstly, we prove a common fixed point result for noncommuting maps. A generalization of Kannan’s fixed point theorem is given in some class of spaces including K-metric spaces.

Hop-by-hop inter-domain routing protocols, such as BGP and IDRP, use independent route selection to realize domains’ local policies. A domain chooses its routes based on path attributes present in a route. It is widely believed that these inter-domain routing protocols always converge. We show that there exist domain policies that cause BGP/IDRP to exhibit persistent oscillations. In these osci...

In this paper, our focus is to acquaint with the Suzuki-type mappings establish some fixed point results using new w-interpolative approach. We present for interpolative contraction operators via w-admissible maps which satisfy Kannan, ?iri?–Reich–Rus, and Hardy–Rogers contractions in quasi-partial b-metric space. Further, outcomes so obtained are affirmed relevant examples.

The aim of the paper is to study some generalizations of weakly Kannan and weakly Chatterjea-type contractive mappings in the setting of partial metric spaces. Some important outcomes are stated and proved, extending classic fixed point and best proximity point theorems. Examples are given in order to emphasize the utility of the main results.

Ajay Kalra • Mengze Shi • Kannan Srinivasan Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Rotman School of Management, University of Toronto, Toronto, Ontario, Canada M5S 3G4 Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 [email protected] • [email protected] • kannans@a...