In this paper, we prove the existence of COMMON FIXED POINT for mappings defined on complete metric spaces with w-distance p satisfying a general contractive inequality of type integral.

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C \rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  $\{\alpha_{n}\}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={\alpha}_{n}{x}_{n}+(1-{\alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize their algorithm and result, imposing some conditions upon the set $C$ and finite many mappings from $C$ in to $H$, to obtain a converging sequence to a COMMON FIXED POINT for these non-self and non-expansive mappings.

In this paper, we define the concept of compatible and weakly compatible mappings in b-metric spaces and inspired by the Ciric and et. al method, we produce appropriate conditions for given the unique COMMON FIXED POINT for a family of the even number of self-maps with together another two self-maps in a complete b-metric spaces. Also, we generalize this COMMON FIXED POINT THEOREM for a sequence with together an even numbers of self-maps in complete b-metric spaces.

In this paper, we introduce the notion of f-weakly compatible mapping for a pair of mappings. A FIXED POINT THEOREM for two pairs of f- weakly compatible mappings satisfying a rational type contraction in a normed space is also established. Subsequently we use our result to find existence of solutions of variational inequalities.