Approximating common fixed points of an evolution family on a metric space via Mann iteration (Q2034529)

Summary: In this article, we present the set of all common fixed points of a subfamily of an evolution family in terms of intersection of all common fixed points of only two operators from the family; that is, for subset \(\mathfrak{M}\) of \(\mathfrak{L} \), we have \(F(\mathfrak{M})= F(\mathfrak{Y}^{(\varrho_1,0)}) \cap F(\mathfrak{Y}^{(\varrho_2,0)})\), where \(\varrho_1\) and \(\varrho_2\) are positive and \((\varrho_1/\varrho_2)\) is an irrational number. Furthermore, we approximate such common fixed points by using the modified Mann iteration process. In fact, we are generalizing the results from a semigroup of operators to evolution families of operators on a metric space.