We give some extensions of the beautiful 1968 fixed point theorem Maia [Maia, M. G. Un’osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 (1968), 139–143] to three classes enriched contractive mappings in Banach spaces: contractions, Kannan contractions and Ćirić-Reich-Rus contractions.

This note extends a recent result of Kannan, Tetali and Vempala to completely solve, via a simple proof, the problem of random generation of a labeled tournament with a given score vector. The proof uses the method of path coupling applied to an appropriate Markov chain on the set of labeled tournaments with the same score vector. MRS: 65C05, 05C20.

Bourgain and Yehudayoff recently constructed O(1)-monotone bipartite expanders. By combining this result with a generalisation of the unraveling method of Kannan, we construct 3-monotone bipartite expanders, which is best possible. We then show that the same graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and have simple thickness 2. All these results are best possible.

In this paper we prove that two local conditions involving the degrees and co-degrees in a graph can be used to determine whether a given vertex partition is Frieze–Kannan-regular. With a more refined version of these two local conditions we provide a deterministic algorithm that obtains a Frieze–Kanan-regular partition of any graph G in time O(|V (G)|).

In this paper, we introduce the concepts of qpb-cyclic-Banach contraction mapping, qpb-cyclic-Kannan mapping and qpb-cyclic β-quasi-contraction mapping and establish the existence and uniqueness of fixed point theorems for these mappings in quasi-partial b-metric spaces. Some examples are presented to validate our results. c ©2016 All rights reserved.

ARJAN DURRESI,VAMSI PARUCHURI, LEONARD BAROLLI, RAJGOPAL KANNAN, S.S IYENGAR Department of Computer Science, Louisiana State University 298 Coates Hall, Baton Rouge, LA 70803, USA Email:{durresi, paruchuri, rkannan, iyengar}@csc.lsu.edu Department of Information and Communication Engineering Faculty of Information Engineering, Fukuoka Institute of Technology (FIT) 3-30-1 Wajiro-Higashi, Higashi...