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.
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Zhang, X. Fixed point theorem of generalized operator quasi-contractive mapping in cone metric space. Afr. Mat. 25, 135–146 (2014). https://doi.org/10.1007/s13370-012-0105-7
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DOI: https://doi.org/10.1007/s13370-012-0105-7