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

Hassen Aydi; M A Barakat; Zoran D Mitrović; Vesna Šešum-Čavić

doi:10.1186/s13660-018-1866-9

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

J Inequal Appl. 2018;2018(1):270. doi: 10.1186/s13660-018-1866-9. Epub 2018 Oct 5.

Authors

Hassen Aydi^{1

2}, M A Barakat³, Zoran D Mitrović^{4

5}, Vesna Šešum-Čavić⁶

Affiliations

¹ 1Department of Mathematics, College of Education in Jubail, Imam Abdulrahman Bin Faisal University, Jubail, Saudi Arabia.
² 2Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
³ 3Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut, Egypt.
⁴ 4Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
⁵ 5Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
⁶ Vienna University of Technology, Institute of Computer Languages, Vienna, Austria.

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.

Keywords: H + -type Pompeiu–Hausdorff metric; Suzuki-type fixed point result; Weak partial metric.