We have been inspired by results of the papers "Important tools and possible applications in metric fixed point theory, Nonlinear Analysis, 47(2001), 3479-3490" by P. P. Murthy, "A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226(1977), 257-290" and "Contractive definitions revisited, Topological methods in non-linear functional analysis, Contemporary Math. A. M. S. 21(1983), 189-205" both by Billy E. Rhoades, "On nonlinear contractions, Proc. Amer. Math. Soc., 20(1969), 458-468" by D. W. Boyd and J. S. W. Wong and "A note on contractive mappings, Proc. Amer. Math. Soc., 13(1962), 459-465" by E. Rakotch.We have presented some fixed points, coincidence points, and common fixed point theorems using different types of contractions which are weaker than Banach's contraction condition in metric and its related spaces such as Partial Ordered Metric Spaces, G-Metric Spaces, Probabilistic Metric Spaces, 2-Metric Spaces and Saks Spaces.

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