Related papers: Cyclic contractions and best proximity pair theore…

This paper has been withdrawn by the author due to a crucial error in several equations.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author due to a crucial error in equation.

The paper was withdrawn by the author. It contained various errors.

This paper has been withdrawn by the author due to some errors.

The paper has been withdrawn by the author due to crucial error in formula (14) which does not satisfy conditions for S(x,y) domain if only d>2.

This paper has been withdrawn by the author, due to necessity of revision.

This paper has been withdrawn by the authors due to some errors.

This paper has been withdrawn by the author(s), due a crucial error on the entanglement of $\Gamma$ registers.

This paper has been withdrawn

We withdraw the paper because the results are wrong.

This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn.

The paper has been withdrawn due to numerical error.

This paper has been withdrawn by the author due to a coming paper completely superseding it.

This paper has been withdrawn due to an error in the proof of the main theorem.

This paper has been withdrawn by the author due to a crucial sign error in equation.

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the author because there is a gap in Lemma 9.

This paper has been withdrawn by the author.