Abstract
We have introduced the new notions of R-weakly graph preserving and R-weakly alpha-admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as alpha-admissible mappings of type S, alpha*-admissible mappings of type S and alpha*- orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b-metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R-weakly alpha-admissible pair of multivalued mappings in a b-metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.