Saadati et al [R. Saadati, S.M. Vaezpour, P. Vetro and B.E. Rhoades,Fixed point theorems in generalized partially ordered G-metricspaces, {\it Mathematical and Computer Modeling,} \textbf{52},797-801, 2010] introduced the notion of $\Omega$-distance mappingsand studied some existing fixed point results. In this paper, weemploy the notion of $\Omega$-distance and some functions defined on$[0,+\infty)$ to introduce some new nonlinear contractions of Suzukitypes. We utilize our new notions to formulate and proved many fixedand common fixed point results. Our results improve and extend manyresults in literature.