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Fixed point theorems for multi-valued mappings with a \(\phi \) function. (English) Zbl 1393.47024

Summary: In this paper, we introduce a new family of mappings from \(\mathbb {R}_{+}^{4}\) to \(\mathbb {R}_{+}\) and it depends on fixed function \(\psi :\mathbb {R}_{+}\rightarrow \mathbb {R}_{+}\), where \(\mathbb {R}_{+}=[0,\infty)\). We call it a \(\Phi_\psi \) family. Then we define a new contractive type condition for multi-valued mappings involving a function \(\phi \in \Phi_\psi \). We also establish some fixed point theorems using our new contractive condition. Our results generalize many existing fixed point theorems.

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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