In this paper, we will present some local fixed point theorems for graphic contractions on a generalized metric space in the sense of Perov.
In this paper we explain the advantage of vector-valued norms and the role of matrices that are convergent to zero in the study of semilinear operator systems by means of some basic methods of nonlinear analysis: the contraction principle, Schauder's fixed point theorem, the Leray-Schauder continuation principle and Krasnoselskii's cone fixed point theorem. A vector version of Krasnoselskii's theorem is also established.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.