Spectral Stability of the $${\overline{\partial }}-$$Neumann Laplacian: Domain Perturbations

We study spectral stability of the $${\bar{\partial }}$$ ∂ ¯ -Neumann Laplacian on a bounded domain in $${\mathbb {C}}^n$$ C n when the underlying domain is perturbed. In particular, we establish upper semi-continuity properties for the variational eigenvalues of the $${\bar{\partial }}$$ ∂ ¯ -Neumann Laplacian on bounded pseudoconvex domains in $${\mathbb {C}}^n$$ C n , lower semi-continuity properties on pseudoconvex domains that satisfy property (P), and quantitative estimates on smooth bounded pseudoconvex domains of finite D’Angelo type in $${\mathbb {C}}^n$$ C n .

FIXED POINTS OF GENERALIZED (ALPHA, PSI,PHI)-CONTRACTIVE MAPS AND PROPERTY(P) IN S-METRIC SPACES

In this paper, we introduce generalized (alpha, psi,phi)-contractive maps and provethe existence and uniqueness of xed points in complete S-metric spaces. We alsoprove that these maps satisfy property (P). We discuss the importance of study of the existence of xed points in S-metric space rather than in the setting of metric space.The results presented in this paper extends several well known comparable results in metric and G-metric spaces. We provide example in support of our result.

Global solvability and regularity for ∂¯ on an annulus between two weakly convex domains which satisfy property (P)

Let [Formula: see text] be a complex manifold of dimension [Formula: see text] and let [Formula: see text]. Let [Formula: see text] be a weakly [Formula: see text]-convex and [Formula: see text] be a weakly [Formula: see text]-convex in [Formula: see text] with smooth boundaries such that [Formula: see text]. Assume that [Formula: see text] and [Formula: see text] satisfy property [Formula: see text]. Then the compactness estimate for [Formula: see text]-forms [Formula: see text] holds for the [Formula: see text]-Neumann problem on the annulus domain [Formula: see text]. Furthermore, if [Formula: see text] is [Formula: see text]-closed [Formula: see text]-form, which is [Formula: see text] on [Formula: see text] and which is cohomologous to zero on [Formula: see text], the canonical solution [Formula: see text] of the equation [Formula: see text] is smooth on [Formula: see text].

Two-dimensional systolic complexes satisfy property A

We show that two-dimensional systolic complexes are quasi-isometric to quadric complexes with flat intervals. We use this fact along with the weight function of Brodzki, Campbell, Guentner, Niblo and Wright [J. Brodzki, S. J. Campbell, E. Guentner, G. A. Niblo and N. J. Wright, Property A and [Formula: see text] cube complexes, J. Funct. Anal. 256(5) (2009) 1408–1431] to prove that two-dimensional systolic complexes satisfy property A.

Fixed points of (α,ψ,φ)-generalized weakly contractive maps and property(P) in S-metric spaces

In this paper, we introduce a notion of (?,?,?)-generalized weakly contractive maps in S-metric spaces and prove the existence of fixed points for such maps. We also prove that these maps satisfy property(P). The results presented in this paper extend the results of Khandaqji, Al-Sharif and Al-Khaleel [15] from G-metric spaces to S-metric spaces. We provide examples in support of our results.

On Local Nilpotency of the Normal Subgroups of a Group

A group G is said to have property μ whenever N is a non-locally nilpotent normal subgroup of G, there is a finite non-nilpotent G-quotient of N. FC-groups and groups with property ν satisfy property μ, where a group G is said to have property ν if every non-nilpotent normal subgroup of G has a finite non-nilpotent G-quotient. HP(G) is the Hirsch-Plotkin radical of G, and Φf(G) is the intersection of all the maximal subgroups of finite index in G (here Φf(G)=G if no such maximal subgroups exist). It is shown that a group G has property μ if and only if HP(G/Φf(G))=HP(G)/Φf(G) and that the class of groups with property ν is a proper subclass of that of groups with property μ. Also, the structure of the normal subgroups of a group: nilpotency with the minimal condition, is investigated.

Common Fixed Point Theorems Satisfying Contractive Type Conditions in Complex Valued Metric Spaces

Some common fixed point theorems satisfying contractive conditions involving rational expressions and product for four mappings that satisfy property (E.A) along with weak compatibility of pairs are proved and further some results using (CLR)-property are obtained in complex valued metric spaces which generalize various results of ordinary metric spaces.

Property (Bb) and Tensor product

In this paper, we find necessary and sufficient conditions for Banach Space operator to satisfy the property (Bb). Then we obtain, if Banach Space operators A ? B(X)and B ? B(Y) satisfy property (Bb) implies A x B satisfies property (Bb) if and only if the B-Weyl spectrum identity ?BW(A x B) = ?BW(A)?(B) U ?BW(B)?(A) holds. Perturbations by Riesz operators are considered.

PropertyPand Some Fixed Point Results on -Weakly ContractiveG-Metric Spaces

We prove some fixed point results for -weakly contractive maps inG-metric spaces, we show that these maps satisfy propertyP. The results presented in this paper generalize several well-known comparable results in the literature.