We build an abstract model, closely related to the stable marriage problem and motivated by Hungarian college admissions. We study different stability notions and show that an extension of the lattice property of stable marriages holds in these more general settings, even if the choice function on one side is not path independent. We lean on Tarski’s fixed point theorem and the substitutability...

The main purpose of this paper is to introduce a generalization of the concept of semi compatible mappings and some fixed point theorems are obtained by using the new notion under strict contractive condition. We also demonstrate that new notion is necessary for the existence of common fixed point.

In this paper, we consider a network in which sessions with long-tailed session lengths arrive as Poisson processes. In particular, we assume that a session of type n transmits rn cells per unit time and lasts for a random time τn with a generalized Pareto distribution given by IP(τn > x) ∼ αnx−(1+βn) for large x, where αn, βn > 0. The network is assumed to be loop-free with respect to source-d...

In this paper we introduce the concept of semi weakly compatibility of maps and establish some common fixed point theorems by using this concept along with the notion of weakly compatibility of maps in the setting of non-complete intuitionistic fuzzy metric spaces. Our results extend and generalize the result of Pant et al [18]. Some related results and illustrative examples have also been disc...

We prove some generic properties for Cr , r = 1, 2, . . . ,∞, areapreserving diffeomorphism on compact surfaces. The main result is that the union of the stable (or unstable) manifolds of hyperbolic periodic points are dense in the surface. This extends the result of Franks and Le Calvez [8] on S to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.

Abstract. We construct a discrete model of the homotopy theory of S-spaces. We define a category P with objects composed of a simplicial set and a cyclic set along with suitable compatibility data. P inherits a model structure from the model structures on the categories of simplicial sets and cyclic sets. We then show that there is a Quillen equivalence between P and the model category of S-spa...