Let φ(z) = (φ1(z), · · · , φn(z)) be a holomorphic selfmap of B and ψ(z) a holomorphic function on B, where B is the unit ball of C n . Let 0 < p, s < +∞,−n− 1 < q < +∞, q+ s > −1 and α ≥ 0, this paper gives some necessary and sufficient conditions for the weighted composition operatorWψ,φ induced by φ and ψ to be bounded and compact between the space F (p, q, s) and α-Bloch space β.

The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk [18] as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K , then T has a fixed point. Alber and Guerre-Delabriere have studied in [3–5] weakly contracti...

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

In this paper, we introduce three classes of proximal contractions that are called the proximally λ−ψ−dominated contractions, generalized ηβγ−proximal and Berinde-type weak obtain common best proximity points for these in setting F−metric spaces. Further, point result α−φ−proximal As an application, fixed coincidence results obtained. Some examples provided to support validity our main results....

The classical interpolation theorem of Craig (cf. e.g. [ChK73]) states that if φ ⇒ ψ is a valid first order predicate logic formula, then there exists a first order formula θ built using only nonlogical symbols occurring in both φ and ψ and, possibly, equality, such that the formulas φ ⇒ θ and θ ⇒ ψ are valid too. A formula θ with this property is called an interpolant between φ and ψ. Similar ...

Banach contraction principle is a fundamental result in fixed point theory and has been applied and extended in many different directions. In 2002, Branciari [3] obtained a fixed point theorem for a single mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Aliouche [2] established a common fixed point theorem for weakly compatible mappings in symme...