Some Generalized Contraction Classes and Common Fixed Points in b-Metric Space Endowed with a Graph

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.

Some Results on (s − q)-Graphic Contraction Mappings in b-Metric-Like Spaces

“…For more details on other generalized metric spaces see [8][9][10][11][12][13][14]. The next proposition helps us to construct some more examples of b-metric (respectively partial b-metric, b-metric-like) spaces.…”

Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications

“…For some recent fixed point results of single valued and multi-valued mappings in a b-metric space, see [9,[14][15][16][17][18]. Throughout this paper, (X, d s ) will denote a complete b-metric space with coefficient s and CB d s (X) the collection of all nonempty closed and bounded subsets of X with respect to d s .…”

H β -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a b

“…Czerwik's contraction was also generalized in many directions to name a few: q-quasi-contraction [15], Hardy-Rogers contraction [16], weak quasi-contraction [17], Ciric contraction [18], etc. More results on multivalued contraction mappings in a b-metric space can be found in [19][20][21][22][23]. Very recently, Debnath [24] proved the set-valued Meir-Keeler-type as well as Geraghty-and Edelstein-type fixed-point theorems in a b-metric space whereas Altun et al [25] and Kumar and Luambano [26] proved fixedpoint results for multivalued F-contraction mappings in complete metric space and partial metric space, respectively.…”