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Fixed point theorems for a semigroup of total asymptotically nonexpansive mappings in uniformly convex Banach spaces

Suantai S., Phuengrattana W.

Opuscula Mathematica

2014

Vol. 34, no. 1

183--197

In this paper, we provide existence and convergence theorems of common fixed points for left (or right) reversible semitopological semigroups of total asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results announced by other authors.

On monoids of injective partial selfmaps almost everywhere the identity

Chuchman I., Gutik O.

Demonstratio Mathematica

2011

Vol. 44, nr 4

699-722

In this paper we study the semigroup (…) of injective partial selfmaps almost everywhere the identity of a set of infinite cardinality (…). We describe the Green relations on (…), all (two-sided) ideals and all congruences of the semigroup (…). We prove that every Hausdorff hereditary Baire topology (…) such that (…) is a semitopological semigroup is discrete and describe the closure of the discrete semigroup (…) in a topological semigroup. Also we show that for an infinite cardinal (…) the discrete semigroup (…) does not embed into a compact topological semigroup and construct two non-discrete Hausdorff topologies turning (…) into a topological inverse semigroup.