We give a condition so that certain mixed monotone mappings on function spaces have a contractive multiplicative relaxation with respect to Thompson’s metric. The corresponding fixed point theorem can be applied to special types of integral equations, for example.

It is well known that the classical contraction mapping principle of Banach is a fundamental result in fixed point theory. Several authors have obtained various extensions and generalizations of Banach’s theorems by considering contractive mappings on different metric spaces. Huang and Zhang [1] have replaced real numbers by ordering Banach space and have defined a cone metric space. They have ...

We obtain existence and uniqueness fixed point theorems as well approximation results for some classes of mappings defined by symmetric contractive type conditions in a convex metric space the sense Takahashi. By using new approach, i.e., technique enrichment mappings, we general which extend known Banach contraction mapping principle from spaces other corresponding enriched on spaces. To indic...

We show that, for a (not necessarily continuous) weakly contractive mean-type mapping $\mathbf{M} \colon I^p\to I^p$ (where $I$ is an interval and $p \in \mathbb{N}$), the functional equation $K \circ \mathbf{M}=K$ has at most one solution in family of continuous means I^p \to I$. Some general approach to latter also given.

Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of E, f : C → C a contractive mapping or a weakly contractive mapping , and T : C → C nonexpansive mapping with the fixed point set F T / ∅. Let {xn} be generated by a...

The main objective of this paper is to deal with some properties of interest in two types of fuzzy ordered proximal contractions of cyclic self-mappings T integrated in a pair (g, T) of mappings. In particular, g is a non-contractive fuzzy self-mapping, in the framework of non-Archimedean ordered fuzzy complete metric spaces and T is a p-cyclic proximal contraction. Two types of such contractio...