Abstract
In this paper, we establish a full statement of Ćirić’s fixed point theorem in the setting of cone metric spaces. More exactly, we obtain a priori and a posteriori error estimates for approximating fixed points of quasi-contractions in a cone metric space. Our result complements recent results of Zhang (Comput. Math. Appl. 62:1627-1633, 2011), Ding et al. (J. Comput. Anal. Appl. 15:463-470, 2013) and others.MSC: Primary 54H25; secondary 47H10, 46A19.
Highlights
1 Introduction In this paper, we study fixed points of quasi-contraction mappings in a cone metric space (X, d) over a solid vector space (Y, )
A unified theory of cone metric spaces over a solid vector space was developed in a recent paper of Proinov [ ]
It is well known that a lot of fixed point results in cone metric setting can be directly obtained from their metric versions
Summary
1 Introduction In this paper, we study fixed points of quasi-contraction mappings in a cone metric space (X, d) over a solid vector space (Y , ). In , Ćirić [ ] introduced contraction mappings and proved the following well known generalization of Banach’s fixed point theorem. ]: Let (X, d) be a cone metric space over a normal solid Banach space (Y , ); every quasi-contraction T of the type ( ) has a unique fixed point in X, and for all x ∈ X the Picard iterative sequence (Tnx) converges to this fixed point.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
