Abstract
We introduce local power contractions and nodal contractions in cone metric spaces and prove the existence of fixed points of such contractions in cone metric spaces. Our theorems generalize the results of Haung and Zhang [L-G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476].
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