Abstract
Abstract In this paper we extend the Banach contraction for multivalued mappings in a cone b-metric space without the assumption of normality on cones and generalize some attractive results in literature. MSC:47H10, 54H25.
Highlights
1 Introduction The analysis on existence of linear and nonlinear operators was developed after the Banach contraction theorem [ ] presented in
In this article we present the generalized form of Cho and Bae [ ] for the case of cone b-metric spaces without normality on cone
Author details 1Department of Mathematics, COMSATS Institute of Information Technology, Chak Shahzad, Islamabad, 44000, Pakistan
Summary
The analysis on existence of linear and nonlinear operators was developed after the Banach contraction theorem [ ] presented in. Rezapour and Hamlbarani [ ] presented the results of [ ] for the case of a cone metric space without normality in cone. Cho and Bae [ ] presented the result of [ ] for multivalued mappings in cone metric spaces with normal cone. In [ ] the authors presented some fixed point results in cone b-metric spaces without assumption of normality on cone. In this article we present the generalized form of Cho and Bae [ ] for the case of cone b-metric spaces without normality on cone. [ ] The results concerning fixed points and other results, in case of cone spaces with non-normal solid cones, cannot be provided by reducing to metric spaces, because in this case neither of the conditions of Lemmas - in [ ] hold.
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