In this paper we prove a fixed point theorem for six mappings in Menger space using the notion of weakly compatible.

We give two examples of the generic approach to fixed point theory. The first example is concerned with the asymptotic behavior of infinite products of nonexpansivemappings in Banach spaces and the second with the existence and stability of fixed points of continuous mappings in finite-dimensional Euclidean spaces.

In this paper, we have given a unique common fixed point theorem for four mappings in a cone metric type space which is a slight variant of theorems of [1, 10]. We also gave an example to illustrate our main theorem. Finally we have given an example in which theorem of [10] is not applicable whereas our corollary is applicable.

In this paper, we prove a common fixed point theorem for single-valued and multivalued mappings on a metric space using the minimal type commutativity condition. We show that continuity of any mapping is not necessary for the existence of a common fixed point.

Recently, the intuitionistic fuzzy stability of Jensen-type functional equation was proved. In this note, we show the intuitionistic fuzzy stability of the Jensen-type functional equation by using the fixed point alternative.

The purpose of this paper is to give a stream-lined proof of the existence and uniqueness of a right-invariant mean on a CHART group. A CHART group is a slight generalisation of a compact topological group. The existence of an invariant mean on a CHART group can be used to prove Furstenberg’s fixed point theorem.

The aim of the present paper is to establish a common fixed point theorem for sequence of self mappings under (φ, ψ)-weak contractions in fuzzy metric space employing the control function which generalizes and improves various well-known comparable results.

This paper discusses the existence of solutions to antiperiodic boundary value problem for nonlinear impulsive fractional differential equations. By using Banach fixed point theorem, Schaefer fixed point theorem, and nonlinear alternative of Leray-Schauder type theorem, some existence results of solutions are obtained. An example is given to illustrate the main result.

The theory of fixed point is a very extensive field, which has various applications. The present paper deals with some developments of Meir-Keeler type fixed point theorem as its remarkable generalizations under several contractive definitions in metric space.

Very recently, Ma et al. (Fixed Point Theory Appl. 2014:206, 2014) introduced C∗-algebra-valued metric spaces as a new concept. Also, Ma and Jiang (Fixed Point Theory Appl. 2015:222, 2015), generalizing this concept, introduced C∗-algebra-valued b-metric spaces. In both frameworks, these and other authors proved some fixed point results. We show in this paper that all these results (as well as ...