A Suzuki-type multivalued contraction on weak partial metric spaces and applications.

Abstract

Based on a recent paper of Beg and Pathak (Vietnam J. Math. 46(3):693-706, 2018), we introduce the concept of $H_q^{+}$ -type Suzuki multivalued contraction mappings. We establish a fixed point theorem for this type of mappings in the setting of complete weak partial metric spaces. We also present an illustrated example. Moreover, we provide applications to a homotopy result and to an integral inclusion of Fredholm type. Finally, we suggest open problems for the class of 0-complete weak partial metric spaces, which is more general than complete weak partial metric spaces.