Related papers: Cyclic contractions and best proximity pair theore…

This paper has been withdrawn by the author due to a crucial mistakes.

This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.

This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.

This article has been withdrawn due to an error in a proof of the main result.

This paper has been withdrawn because of serious errors.

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.

This paper has been withdrawn by the author due to a crucial error in equation (51).

The paper is withdrawn by the author due to a recently discovered flaw in a basic proof.

This paper has been withdrawn by the authors due to an error in the main theorem.

This paper has been withdrawn by the author due to an error.

This paper has been withdrawn by the author, due to an error in Proposition 2.2.

This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.

This paper has been withdrawn by the author due to an error

This paper has been withdrawn by the author, due a crucial error in the optimization. For the last one month I have been trying to remove the error, but it seems to take a lot of time so I decided to withdraw this paper for the moment.

This paper has been withdrawn by the authors, due a crucial error.

This paper has been withdrawn by the authors due to an error.

The paper is being withdrawn because of some theoretical inconsistencies.

This paper has been withdrawn by the author due to essential mistakes in some previous versions.

This paper has been withdrawn by the authors, because of serious experimental problems.