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This paper discusses nonlinear discrete-time maps of the form x(k+1)=F(x(k)), focussing on equilibrium points of such maps. Under some circumstances, Lefschetz fixed-point theory can be used to establish the existence of a single locally attractive equilibrium (which is sometimes globally attractive) when a general property of local attractivity is known for any equilibrium. Problems in social networks often involve such discrete-time systems, and we make an application to one such problem.

Nonlinear Mapping Convergence and Application to Social Networks