On generalized convex contractions of type-2 in b-metric and 2-metric spaces

In this paper, we present the notion of generalized convex contraction mapping of type-2, which includes the generalized convex contraction (resp. generalized convex contraction of order-2) of Miandaragh et al. [M. A. Miandaragh, M. Postolache, S. Rezapour, Fixed Point Theory Appl., 2013 (2013), 8 pages] and the convex contraction mapping of type-2 of Istratescu [V. I. Istratescu, I, Libertas Math., 1 (1981), 151–163]. Utilizing this class of mappings, we establish approximate fixed point and fixed point theorems in the setting of b-metric and 2-metric spaces.