We prove common fixed point theorems for two pairs of hybrid mappings satisfying implicit relations in complete metric spaces using the concept of R−weak commutativity of type AT and we correct errors of [1], [3] and [8]. Our theorems generalize results of [1-3], [8], [12-16] and [21].

One challenging problem that children overcome in learning new words is recognizing the hierarchical category of a label. For instance, one object could be called a Dalmatian, a dog, or an animal. Xu and Tenenbaum (2007) proposed a Bayesian model to explain how 3.5 to 5-year-olds solve this ambiguity. They emphasized children's appreciation for “suspicious coincidences:” a label applied to thre...

We prove that there is a coincidence index for the inclusion F (x) ∈ Φ(x) when Φ is convex-valued and satisfies certain compactness assumptions on countable sets. For F we assume only that it provides a coincidence index for single-valued finite-dimensional maps (e.g. F is a Vietoris map). For the special case F = id, the obtained fixed point index is defined if Φ is countably condensing; the a...

Suppose X is a partially ordered real Banach space such that there is a 2−norm on X. The purpose of this paper is to prove coupled coincidence and coupled common fixed point theorems for mappings from X ×X to X.

In this paper, tripled coincidence points of mappings satisfying some nonlinear contractive conditions in the framework of partially ordered Gb-metric spaces are obtained. Our results extend the results of Aydi et al. (Fixed Point Theory Appl., 2012:101, 2012, doi:10.1186/1687-1812-2012-101). Moreover, some examples of the main result are given. Finally, some tripled coincidence point results f...

In this paper, we prove coupled coincidence points and common fixed points theorem for two mappings satisfying various contractive conditions in partially ordered metric spaces. Our results will generalize and extend some recent results in fixed point theory.

The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are sufficient to characterize the coincidence index in the setting of continuous m...