Abstract

In this article, by introducing a new operator, we give a new generalized contraction condition for multivalued maps. Moreover, without assumption of lower semi-continuity, we prove some fixed point theorems in incomplete metric spaces. Our results are extension of the corresponding results of I. Altun et al.\ (Nonlinear Analysis: Modeling and control, 2016, Vol.\ 21, No.\ 2, 201--210). Also, we provide some examples to show that our main theorem is a generalization of some previous results.

Keywords: Fixed point; Hausdorff metric; multivalued contraction; $SO$-complete metric space; $SO$-lower semi-continuous.

MSC: 54H25, 47H10

Pages:  369$-$377     

Volume  71 ,  Issue  4 ,  2019