Fixed point theorems without continuity of any mappings in dislocated quasi metric space (Q2873056)

The first two fixed point theorems of this paper involve selfmaps of a complete quasi-dislocated (dq) metric space. Unfortunately, the proof of the first theorem (Theorem 3.1) is incomplete. The authors show that \(d(Tz, z) = 0\), but fail to also show that \(d(z, Tz) = 0\). The same omission occurs in the attempted proof of the uniqueness of the fixed point. Also, the proof of the second theorem (Theorem 3.2) is incorrect, since the authors tacitly assume that \(d(x_n, x_n) = 0\). The same error is made in the proof of the third theorem (Theorem 3.3).NEWLINENEWLINEReviewer's comment: I have a correct proof of Theorem 3.2. Whether or not Theorem 3.3 is a true statement remains an open question.