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Some new fixed point results for multi-valued weakly Picard operators

Aydi Hassen (Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam + Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)
Felhi Abdelbasset (Department of Mathematics and Physics, Preparatory Engineering Institute, Bizerte, Carthage University, Tunisia)
Karapınar Erdal (Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan)
Alshahrani Hind S. (Imam Abdulrahman Bin Faisal University, Department of Mathematics, College of Education of Jubail, Industrial Jubail, Saudi Arabia)

In this paper, we present some extensions of Banach contraction principle for multi-valued maps. Corresponding convergence theorems for the Picard iteration associated to a class of multi-valued operators are obtained in the setting of modular metric spaces. The presented results improve many recent fixed points results in the setting of modular metric spaces and also generalize some classical known results. Moreover, some examples are given.

Keywords: modular metric spaces, Δ2-condition, multi-valued mapping, fixed point