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α-ψ-Geraghty contraction type mappings and some related fixed point results

Karapınara Erdal (Atilim University, Department of Mathematics, Ankara Turkey)

In this paper, we consider a generalization of α-ψ-Geraghty contractions and investigate the existence and uniqueness of fixed point for the mapping satisfying this condition. We illustrate an example and an application to support our results. In particular, we extend, improve and generalize some earlier results in the literature on this topic.

Keywords: fixed point, differential equations, generalized α-ψ-Geraghty contractions