# Some Fixed Point Results for Multivalued Mappings in b-Multiplicative and b-Metric Space

## Main Article Content

### Abstract

The main outcome of this paper is to introduce the notion of Hausdorff b-multiplicative metric space and to present some fixed point results for multivalued mappings in this space. Moreover, we obtain some fixed point results satisfying rational type contractive condition on closed ball for multivalued mappings in b-metric space.The proven results are original in nature.

## Article Details

### References

- M. Abbas, B. Ali, and YI. Suleiman, Common Fixed Points of Locally Contractive Mappings in Multiplicative Metric Spaces with Application, Int. J. Math. Math. Sci. 2015 (2015), Article ID 218683.
- M. Abbas, M. D. Sen, and T. Nazir, Common Fixed Points of Generalized Rational Type Cocyclic Mapping in Multiplicative Metric Spaces, Discrete Dynamics in Nature and Society, 2015 (2015), ID 532725.
- A. E. Al-Mazrooei, D. Lateef, and J. Ahmad, Common Fixed Point Theorems for Generalized Contractions, J. Math. Anal. 8 (3) (2017), 157-166.
- M. U. Ali, T. Kamran, and A. Kurdi, Fixed Point in b-multiplicative Metric Spaces, U.P.B. Sci. Bull. Ser. A, 79 (3) (2017), 107-116.
- M. Arshad, A. Shoaib, M. Abbas and A. Azam, Fixed Points of a Pair of Kannan Type Mappings on a Closed Ball in Ordered Partial Metric Spaces, Miskolic Math. Notes, 14 (3) (2013), 769-784.
- I. A. Bakhtin, The Contraction Mapping Principle in Almost Metric Spaces, Funct. Anal. 30 (1989), 26-30.
- S. Czerwick, Contraction Mapping in b-metric Spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5-11.
- C. Mongkolkeha, and W. Sintunaravat, Optimal Approximate Solutions for Multiplicative Proximal Contraction Mappings in Multiplicative Metric Spaces, Proc. Nat. Acad. Sci. 86 (1) (2016), 15-20.
- C. Mongkolkeha, and W. Sintunavarat, Best Proximity Points for Multiplicative Proximal Contraction Mapping on Multiplicative Metric Spaces, J. Nonlinear Sci. Appl. 8 (6) (2015), 1134-1140.
- M. Ozavsar and A. C. Cervikel, Fixed Points of Multiplicative Contraction Mappings on Multiplicative Metric Spaces, arXiv:1205.5131v1 [math.GM], 2012.
- M. Sarwar, and M. Rahman, Fixed Point Theorems for Ciric's and Generalized Contractions in b-metric spaces, Int. J. Anal. Appl. 7 (1) (2015), 70-78.
- A. Shoaib, A. Azam, M. Arshad, and E. Ameer, Fixed Point Results For Multivalued Mappings on a Sequence in a Closed Ball with Application, J. Math. Computer Sci. 17 (2017), 308-316.
- A Shoaib, P Kumam, A Shahzad, S Phiangsungnoen, Q Mahmood, Fixed Point Results for Fuzzy Mappings in a b-metric Space. Fixed Point Theory Appl. 2018 (2018), 2.
- A. Shoaib, M. Arshad, and A. Azam, Fixed Points of a Pair of Locally Contractive Mappings in Ordered Partial Metric Spaces. Mat. Vesnik, 67 (1) (2015), 26-38.
- A. Shoaib, M. Arshad and M. A. Kutbi, Common Fixed Points of a Pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Partial Metric Spaces. J. Comput. Anal. Appl. 17 (2) (2014), 266-264.