Common fixed point for generalized multivalued mappings via simulation function in metric spaces
Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1107-1121
https://doi.org/10.4134/CKMS.c190388
Published online August 13, 2020
Printed October 31, 2020
Swati Antal, U. C. Gairola
H. N. B. Garhwal University, BGR Campus; H. N. B. Garhwal University, BGR Campus
Abstract : The purpose of this paper is to introduce the notion of generalized multivalued $\mathcal{Z}$-contraction and generalized multivalued Suzuki type $\mathcal{Z}$-contraction for pair of mappings and establish common fixed point theorems for such mappings in complete metric spaces. Results obtained in this paper extend and generalize some well known fixed point results of the literature. We deduce some corollaries from our main result and provide examples in support of our results.
Keywords : Complete metric space, multivalued mapping, generalized $\mathcal{Z}$-contraction for pair of mappings, generalized Suzuki type $\mathcal{Z}$-contraction for pair of mappings, simulation function, common fixed point
MSC numbers : Primary 47H10, 54H25
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