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

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

Author information

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

Conflict of interest statement

The authors declare that they have no competing interests.

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