title: Fixed point theorems for generalized α -β-weakly contraction mappings in metric spaces and applications.
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.
authors.affiliation: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
authors.forename: Abdul
authors.initials: A
authors.lastname: Latif
authors.affiliation: Department of Mathematics, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhon Pathom 73140, Thailand.
authors.forename: Chirasak
authors.identifier: 0000-0002-0120-2240
authors.initials: C
authors.lastname: Mongkolkeha
authors.affiliation: Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12121, Thailand.
authors.forename: Wutiphol
authors.identifier: 0000-0002-0932-1332
authors.initials: W
authors.lastname: Sintunavarat