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

Reny George, Hossam A. Nabwey, Rajagopalan Ramaswamy and Stojan Radenović
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Reny George: Department of Mathematics, College of Science, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Hossam A. Nabwey: Department of Mathematics, College of Science, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Rajagopalan Ramaswamy: Department of Mathematics, College of Science, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Stojan Radenović: Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Mathematics, 2019, vol. 7, issue 8, 1-19

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.

Keywords: (?, ?*, G , ? s ) contractions; directed graph; R -Weakly graph preserving; rational contractions; R -weakly ? -admissible (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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