FITTING SUBGROUP AND NILPOTENT RESIDUAL OF FIXED POINTS

Diagonal arguments and fixed points

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Coupled fixed points of generalized Kanann contraction and its applications

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...

Monodromy and Stability for Nilpotent Critical Points

We give a new and short proof of the characterization of monodromic nilpotent critical points.We also calculate the first generalized Lyapunov constants in order to solve the stability problem. We apply the results to several families of planar systems obtaining necessary and sufficient conditions for having a center. Our method also allows us to generate limit cycles from the origin.

Approximating fixed points of generalized nonexpansive mappings