Matthews (1994) introduced a new distance "Equation missing"<!-- image only, no MathML or LaTex --> on a nonempty set "Equation missing"<!-- image only, no MathML or LaTex -->, which is called partial metric. If "Equation missing"<!-- image only, no MathML or LaTex --> is a partial metric space, then "Equation missing"<!-- image only, no MathML or LaTex --> may not be zero for "Equation missing"<!-- image only, no MathML or LaTex -->. In the present paper, we give some fixed point results on these interesting spaces.

We present some fixed point results for nondecreasing and weakly increasing operators in a partially ordered metric space using implicit relations. Also we give an existence theorem for common solution of two integral equations.

Recently, Wardowski [15] introduced the concept of F-contraction on complete metric space. This type contraction is proper generalization of ordinary contraction. In the present paper, we give some fixed point results for generalized F-contractions including Ciric type generalized F-contraction and almost F-contraction on complete metric space. Also, we give some illustrative examples.