Dislocated metric and fixed point theorems

The paper deals with the here defined dislocated strong quasi-metric (if $p(y,x)= 0$ p ( y , x ) = 0 , then $x=y$ x = y ; 0 ≤ p(z,x) ≤ p(z,y) + p(y,x) 0 ≤ p ( z , x ) ≤ p ( z , y ) + p ( y , x ) ) and with the well-known notion of the dislocated metric (in addition, $p(y,x)= p(x,y)$ p ( y , x ) = p ( x , y ) ). In particular, the partial metric is a kind of dislocated metric. Our basic results on general contractions (also for cyclic mappings) and results of variational type can be treated as a starting point for further development.