This is a brief review of some of the things, both past and present, which have motivated the writer’s interest in metric fixed point theory.

In this paper we obtain a unique common fixed point theorem for three pairs of weakly compatible mappings in D∗-cone metric spaces.

New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.

*Correspondence: [email protected] 1Institute of Applied Mathematics, Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China Full list of author information is available at the end of the article Abstract In this paper, we consider the setting of multiplicative metric spaces to establish results regarding the common fixed points of four mappings, using a contrac...

We prove a common fixed point theorem for two multifunctions defined on a closed ball of a complete metric space with values in the set of all nonempty and closed subsets of this space, multifunctions which satisfy an implicit contractive relation of Latif-Beg type.

In this paper, we introduce the notion of (α,HLC , fRC)-Caristi type contraction mappings and prove fixed point theorem by using this notion on complete metric space. To illustrate our result, we construct an example.

In this paper, we introduce cyclic weak φ−contractions in fuzzy metric spaces and utilize the same to prove some results on existence and uniqueness of fixed point in fuzzy metric spaces. Some related results are also proved besides furnishing illustrative examples.

*Correspondence: [email protected] Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia Abstract We study the existence and uniqueness of fixed points for self-operators defined in a b-metric space and belonging to the class of (α,ψ )-type contraction mappings. The obtained results generalize and unify several existing fixed point theor...

The purpose of this paper is to present a fixed point theorem for cyclic weak contractions in compact metric spaces. c ©2013 All rights reserved.

Let ∆ be the ball |x| < 1 in the complex vector space C, let f : ∆ → C be a holomorphic mapping and let M be a positive integer. Assume that the origin 0 = (0, . . . , 0) is an isolated fixed point of both f and the M -th iteration f of f . Then for each factor m of M, the origin is again an isolated fixed point of f and the fixed point index μfm(0) of f m at the origin is well defined, and so ...