Mustefa Abduletif - Department of Mathematics, Jimma University
Kidane Koyas - Department of Mathematics, Jimma University
Solomon Teweldemedhin - Department of Mathematics, Jimma University

In this paper, first, we introduce (\alpha,\psi,\varphi) -Geraghty and generalized (\alpha,\psi,\varphi) -Geraghty contraction mappings in b-metric spaces and then we prove the existence and uniqueness of fixed point after exploring all the conditions which guarantee the existence of fixed point. Our results extend and generalize related fixed point results in the existing literature. We also provide examples in support of our main findings.

\alpha-admissible mapping, generalized (\alpha,\ psi, \varphi)-Geraghty Contraction, b-metric space