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Fixed point theorems for generalized α -β-weakly contraction mappings in metric spaces and applications
Abdul Latif1, Chirasak Mongkolkeha2, Wutiphol Sintunavarat3
1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
Abstract:
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.
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