In this paper, we prove the existence of the attractors for Reich's iterated function systems by virtue of a Banach-like fixed point theorem. As a result, under the condition that the Reich contractions discussed are continuous, we give an affirmative answer to an open question posed by Singh et al. in 2009. In addition, we formulate a collage theorem for Reich's iterated function systems. MSC: 47H10; 54HA25

In this note we correct some errors that appeared in the article (Han and Xu in Fixed Point Theory Appl. 2013:3, 2013) by modifying some conditions in the main theorems and corresponding corollaries. MSC: 47H10; 54H25

In this article, without requiring solidness of the underlying cone, a kind of new convergence for sequences in cone b b -metric spaces over Banach algebras and a new kind of completeness for such spaces, namely, wrtn-completeness, are introduced. Under the condition that the cone b b -metric spaces are wrtn-complete and the underlying cones are normal, we establish a common fixed point theorem of contractive conditions with vector-valued coefficients in the non-solid cone b b -metric spaces over Banach algebras, where the coefficients s ≥ 1 s\ge 1 . As consequences, we obtain a number of fixed point theorems of contractions with vector-valued coefficients, especially the versions of Banach contraction principle, Kannan’s and Chatterjea’s fixed point theorems in non-solid cone b b -metric spaces over Banach algebras. Moreover, some valid examples are presented to support our main results.