Corpus ID: 16875679

FIXED POINT THEOREMS FOR NONSELF SINGLE-VALUED ALMOST CONTRACTIONS

@inproceedings{Berinde2013FIXEDPT,
  title={FIXED POINT THEOREMS FOR NONSELF SINGLE-VALUED ALMOST CONTRACTIONS},
  author={Vasile Berinde and Madalina Pacurar},
  year={2013}
}
Let X be a Banach space, K a non-empty closed subset of X and let T : K → X be a non-self almost contraction. The main result of this paper shows that if T has the so called property (M) and satisfies Rothe’s boundary condition, i.e., maps ∂K (the boundary of K) into K, then T has a fixed point in K. This theorem generalizes several fixed point theorems for non-self mappings and also extends several important results in the fixed point theory of self mappings to the case on non-self mappings. 

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