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Fixed point theorems for a new generalization of contractive maps in incomplete metric spaces and its application in boundary value problems

Zahra Ahmadi, Rahmatollah Lashkaripour and Hamid Baghani

Abstract

In this paper, we obtain some fixed point theorems for multivalued mappings in incomplete metric spaces. Moreover, as motivated by the recent work of Olgun, Minak and Altun [M. Olgun, G. Minak and I. Altun, A new approach to Mizoguchi–Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 2016, 3, 579–587], we improve these theorems with a new generalization contraction condition for multivalued mappings in incomplete metric spaces. This result is a significant generalization of some well-known results in the literature. Also, we provide some examples to show that our main theorems are a generalization of previous results. Finally, we give an application to a boundary value differential equation.

MSC 2010: 11K55; 37C25

References

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Received: 2020-01-13
Accepted: 2020-07-28
Published Online: 2021-02-02
Published in Print: 2021-12-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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