Abstract This paper provides two wide classes of contractions, which are obtained by using notions $\alpha _{s^{p}} $ α s p -admissibility and the rich set C -class functions in setting a complete b -metric-like space under more g...

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop notion $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points a new type contractive mappings complete metric spaces,} Fixed Point Theory Appl., 94, (2012)). To achieve this, introduce Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator also...

We consider contractive homomorphisms of a planar algebra A(Ω) over a finitely connected bounded domain Ω ⊆ C and ask if they are necessarily completely contractive. We show that a homomorphism ρ : A(Ω) → B(H) for which dim(A(Ω)/ ker ρ) = 2 is the direct integral of homomorphisms ρT induced by operators on two dimensional Hilbert spaces via a suitable functional calculus ρT : f 7→ f(T ), f ∈ A(...

This paper deals with families of matrix-valued Aleksandrov--Clark measures $\{\boldsymbol{\mu}^\alpha\}_{\alpha\in\mathcal{U}(n)}$, corresponding to purely contractive $n\times n$ matrix functions $b$ on the unit disc complex plane. We do not make other apriori assumptions $b$. In particular, may be non-inner and/or non-extreme. The study such is mainly motivated from applications unitary fini...

We said that φ is n-positive if φn is positive and that φ is completely positive if φn is positive for all n. The map φ is said to be n-bounded (resp., n-contractive) if ‖φn‖ ≤ c (resp., ‖φn‖ ≤ 1). The map φ is said to be completely bounded (resp., completely contractive) if ‖φ‖cb = supn‖φ‖n <∞ (resp., ‖φ‖cc = supn‖φn‖ ≤ 1). npositivity (resp., n-boundedness or n-contractivity) implies (n−1)-po...

A systematic framework for analyzing dynamical attributes of games has not been well-studied except the special class potential or near-potential games. In particular, existing results have shortcomings in determining asymptotic behavior a given dynamics designated game. Although there is large body literature on developing convergent to Nash equilibrium (NE) game, general, an underlying may be...

We introduce Suzuki type P-contractive mappings by taking into account the concepts of contractive, P-contractive, and contractive mappings. Then, for such on compact metric spaces, we present a fixed point theorem that is more general than well-known Edelstein theorem.

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups which are not necessarily locally connected. These results are local analogues of...