Existence and Ulam–Hyers stability of fixed point problem of generalized Suzuki type $$( \alpha _{*}{,\psi }_{\varphi })$$ ( α ∗ , ψ φ ) -contractive multivalued operators

Abstract

The aim of this paper is to introduce a class of generalized Suzuki type \( (\alpha _{*},\psi _{\varphi })\)-contractive multivalued operators and to prove the existence of fixed point and common fixed point of such operators in the setup of b-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. An estimate of Hausdorff distance between the fixed point sets of two generalized Suzuki type \((\alpha _{*},\psi _{\varphi })\)-contractive multivalued operators is obtained. We further investigate the Ulam–Hyers stability of fixed point problem of operators considered herein in the framework of b-metric spaces.