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We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized  α - β -weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.

Fixed Point Theorems for Generalizedα-β-Weakly Contraction Mappings in Metric Spaces and Applications