Recently, Zhang and Song [Q. Zhang, Y. Song, Fixed point theory forgeneralized $varphi$-weak contractions,Appl. Math. Lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. In this paper, we prove a common fixed point theorem fora family of compatible maps. In fact, a new generalization of Zhangand Song's theorem is given.

When moving to a Type Theory without proof-irrelevance the notion of a setoid has to be generalized to the notion of a weak ω-groupoid. As a first step in this direction we study the formalisation of weak ω-groupoids in Type Theory. This is motivated by Voevodsky’s proposal of univalent type theory which is incompatible with proof-irrelevance and the results by Lumsdaine and Garner/van de Berg ...

In this paper, we introduce the notion of weak $psi$-quasi contraction in generalized metric spaces and using this notion we obtain conditions for the existence of fixed points of a self map in $D$-complete generalized metric spaces. We deduce some corollaries from our result and provide examples in support of our main result.

In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators [Formula: see text] in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutator...

The concept of generalized KKM maps was initiated by Kassay-Kolumbán in 1990 and Chang-Zhang 1991. Recently, Balaj his colleagues extended w.r.t. a multimap to weak applied them various problems the theory. However, their results are mainly concerned within realm topological vector spaces. Our aim this article is extend some abstract convex Some related facts also discussed.