Some new fixed point theorems for a family of mappings are obtained and applied to problems on sets with convex sections that were first studied by Ky Fan.

A point x ∈ C is a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T ; that is, F(T)= {x ∈ C : Tx = x}. Also, recall that a family S= {T(s) | 0≤ s <∞} of mappings from C into itself is called an asymptotically nonexpansive semigroup on C if it satisfies the following conditions: (i) T(0)x = x for all x ∈ C; (ii) T(s+ t)= T(s)T(t) for all s, t ≥ 0; (iii) there exists ...

Sufficient conditions for the existence of a common fixed point for uniformly Cq− commuting mappings satisfying a generalized contractive conditions in the framework of a convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various known results in the literature.

In this paper, we give some definitions and conclusions in dislocated quasimetric spaces. Also, we establish two fixed point theorems for multivalued mappings in these spaces.

Some results regarding the existence of a fixed point for a multivalued non-expansive mapping defined on an unbounded subset of a reflexive Banach space are established.

The alternation hierarchy problem asks whether every μ-term φ, that is, a term built up also using a least fixed point constructor as well as a greatest fixed point constructor, is equivalent to a μ-term where the number of nested fixed points of a different type is bounded by a constant independent of φ. In this paper we give a proof that the alternation hierarchy for the theory of μ-lattices ...

In this work, we give a characterization of the existence of minimal elements in partially ordered sets in terms of fixed point of multivalued maps. This characterization shows that the assumptions in Caristi’s fixed point theorem can, a priori, be weakened. Finally, we discuss Kirk’s problem on an extension of Caristi’s theorem and prove a new positive result which illustrates the weakening me...

We prove some fixed point theorems for nonexpansive selfand non-self-mappings in product spaces; in particular, we provide a constructive proof of a result of Kirk and Martinez and a partial answer to a question of Khamsi. Our proofs are elementary in the sense that we do not use any universal (or ultra) nets.