SOME FIXED POINT AND COMMON FIXED POINT RESULTS THROUGH Ω-DISTANCE UNDER NONLINEAR CONTRACTIONS

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