Coincidence points of multivalued \(f\)-almost nonexpansive mappings (Q2845223)

Let \((X,d)\) be a metric space. A set-valued map \(T:X\longrightarrow \mathcal{CB}(X)\) is called a multivalued weak contraction, see \textit{M. Berinde} and \textit{V. Berinde} [J. Math. Anal. Appl. 326, No. 2, 772--782 (2007; Zbl 1117.47039)], if there exist a constant \(\delta\in (0,1)\) and some \(L\geq 0\) such that NEWLINE\[NEWLINE H(Tx, Ty)\leq\delta\cdot d(x,y)+L d(y,Tx) \quad\text{for all}\;x,y\in X, NEWLINE\]NEWLINE where \(H:\mathcal{CB}(X)\times \mathcal{CB}(X) \rightarrow [0,\infty)\) is the Pompeiu-Hausdorff distance induced by the distance \(d\). In the last years, this class of mappings has been intensively studied by various authors. In the paper under review, the author considers a more general class of multivalued weak contractive type mappings, i.e., the class of generalised multivalued \((f,\theta,L)\)-almost contractions, and establishes coincidence point theorems and common fixed point theorems for this new class of mappings.