A hybrid class of expansive-contractive mappings in cone b-metric spaces

Abstract

In this research work, we generalize classical results on the existence of common fixed points of generalized expanding mappings by removing the constraint on the signs of the underlining coefficients in the inequality considered. The hybrid class obtained surprisingly regroups both classes of generalized contractive maps and classes of generalized expansive maps. The research work also provides a clear understanding of the boundary between contractive and expansive mappings in literature and is applied to product metric-type spaces.

Fixed point theorems for generalized contraction mappings on b-rectangular metric spaces

“…These pairs of generalized mappings were extended by Olaoluwa and Olaleru in [18], but in the framework of b-metric spaces and for a pair of four mappings, as follows…”

“…Now, we present an useful lemma for expansive-type mappings in b-rectangular metric spaces, following the technique used in [18]. Lemma 2.7.…”