Abstract
We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as α -admissible mappings of type S, α * -admissible mappings of type S and α * - 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 α -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.
Highlights
In recent years three important tools have been successfully utilized in fixed point theory to generalize fixed point theorems for single-valued mappings and multi valued mappings
In the present work using C-class functions and some modified versions of control functions as in George et al [3], we have introduced generalized classes of contractions and rational contractions for a pair of multivalued mappings and proved common fixed point theorems in a b-metric space endowed with a graph
We introduce the classes of (C, Ψ∗, G, γs) and (C, Ψ∗, G, γ) contractions and rational contractions and prove common fixed point theorems in b-metric space endowed with a graph
Summary
In recent years three important tools have been successfully utilized in fixed point theory to generalize fixed point theorems for single-valued mappings and multi valued mappings. Later Phonon et al [9] generalised the concept of a graph preserving mapping by introducing weak graph preserving mapping and proved fixed point theorems for multivalued mappings in a metric space endowed with a graph More results in this direction were considered wherein. Extending these concepts to the case of multivalued mappings, Ameer et al [23] introduced α∗ -admissible and α∗ -orbital admissible multivalued mappings whereas Haitham et al [2] introduced α-admissible multivalued mappings of type S in a b-metric space In all these works the authors proved fixed point theorems for the corresponding α-admissible type of mappings satisfying various contraction conditions. Our main results and its consequences are improved, generalized and extended versions of many results appearing in literature
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
