Fixed point theorem of generalized operator quasi-contractive mapping in cone metric space

Fixed point theorem of generalized operator quasi-contractive mapping in cone metric space In this paper, we use bounded linear operators and the convexity in Banach space, introduce a new generalized operator quasi-contractive condition, prove a new fixed point theorem in cone metric space. The conclusion in this paper unify, improve and generalize many contractive-type and quasi-contractive-type fixed point theorems in metric spaces and cone metric spaces. A example is given, which explains that the operator versions contractive condition is real generalization of scalar versions contractive condition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Afrika Matematica Springer Journals

Fixed point theorem of generalized operator quasi-contractive mapping in cone metric space

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2012 by African Mathematical Union and Springer-Verlag
Subject
Mathematics; Mathematics, general; Applications of Mathematics; History of Mathematical Sciences; Mathematics Education
ISSN
1012-9405
eISSN
2190-7668
D.O.I.
10.1007/s13370-012-0105-7
Publisher site
See Article on Publisher Site

Abstract

In this paper, we use bounded linear operators and the convexity in Banach space, introduce a new generalized operator quasi-contractive condition, prove a new fixed point theorem in cone metric space. The conclusion in this paper unify, improve and generalize many contractive-type and quasi-contractive-type fixed point theorems in metric spaces and cone metric spaces. A example is given, which explains that the operator versions contractive condition is real generalization of scalar versions contractive condition.

Journal

Afrika MatematicaSpringer Journals

Published: Sep 16, 2012

References

  • Cone metric spaces and fixed point theorems of contractive mappings
    Huang, LG; Zhang, X

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