A generalization of Matkowski's fixed point theorem and Istratescu's fixed point theorem concerning convex contractions

作者：Miculescu Radu^*; Mihail Alexandru

来源：Journal of Fixed Point Theory and Applications, 2017, 19(2): 1525-1533.

DOI：10.1007/s11784-017-0411-7

• Matkowski's fixed point theorem
• Istratescu's fixed point theorem
• b-metric spaces
• comparison functions
• convex contractions

In this paper we obtain a generalization of Matkowski's fixed point theorem and IstrA escu's pound fixed point theorem concerning convex contractions. More precisely, given a complete b-metric space (X, d) we prove that every continuous function is a Picard operator, provided that there exist and a comparison function such that for all . In addition, we point out that if , taking into account that a metric space is a b-metric space, we obtain a generalization of Matkowski's fixed point theorem. Moreover, we prove that IstrA escu's pound fixed point theorem concerning convex contractions is a particular case of our result for . By providing appropriate examples we show that the above-mentioned two generalizations are effective.

• 出版日期2017-6