Multivalued (g − F − φ) contractions obtaining common fixed points in G-metric spaces

The aim of this paper is to introduce new notions called generalized [Formula: see text] contraction and rational type [Formula: see text] contraction for hybrid maps in complete G-metric spaces. First, using new concept of generalized [Formula: see text] contraction we establish a common fixed point theorem for a hybrid pair of weakly compatible maps. Second, we prove a common fixed point theorem for occasionally coincidentally idempotent mappings satisfying another new concept of rational type [Formula: see text] contraction under common limit range property. Our results generalize and improve several known results of the existing literature. Also, we give an example to indicate the usefulness of our main results.