‎‎Many authors such as Amini-Harandi‎, ‎Rezapour ‎et al., ‎Kadelburg ‎et al.‎‎, ‎have tried to find at least one fixed point for quasi-contractions when $alphain[frac{1}{2}‎, ‎1)$ but no clear answer exists right now and many of them either have failed or changed to a lighter version‎. In this paper‎, ‎we introduce some new strict fixed point results in the set of multi-valued '{C}iri'{c}-gener...

Abstract. We define a stronger property than unique ergodicity with respect to the fixed–point subalgebra firstly investigated in [1]. Such a property is denoted as F–strict weak mixing (F stands for the Markov projection onto the fixed–point operator system). Then we show that the free shifts on the reduced C–algebras of RD–groups, including the free group on infinitely many generators, and am...

The author uses fixed point index properties and Inspired by the work in Benmezai Boucheneb (see Theorem 3.8 [3]) to prove new theorems for strict set-contraction defined on a Banach space leaving invariant cone.