New fixed point theorems in midconvex subgroups of abelian Banach groups

Document Type : Research Paper


Department of Mathematics, Payame Noor University, P.O.BOX 19395-3697, Tehran, Iran.


In this paper, using continuous, injective, and sequentially convergent mappings on a group, new generalizations of Kannan and Chatterjea's fixed points in Banach groups are presented. we generalize contractions with constants to prove some fixed point theorems in a Banach group. Moreover, nondecreasing continuous functions from the set of positive real numbers to itself are used to introduce a new extension of contractions on normed groups.