We study harmonic Bergman functions on the upper half-space of Rn. Among our main results are: The Bergman projection is bounded for the range 1 < p <∞; certain nonorthogonal projections are bounded for the range 1 ≤ p < ∞; the dual space of the Bergman L1-space is the harmonic Bloch space modulo constants; harmonic conjugation is bounded on the Bergman spaces for the range 1 ≤ p <∞; the Bergma...

In a paper [1] the authors ask whether the Frobenius and the H norms are induced. There they claimed that the Frobenius norm is not induced, and consequently conjectured that the H-norm may not be induced. In this note it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the H-norm is in fact induced on a particular matrix-valued L1 space. NOTATION R...

One of the most remarkable basis of the gravity data inversion is the recognition of sharp boundaries between an ore body and its host rocks during the interpretation step. Therefore, in this work, it is attempted to develop an inversion approach to determine a 3D density distribution that produces a given gravity anomaly. The subsurface model consists of a 3D rectangular prisms of known sizes ...

Some algorithms for nding common xed point of a family of mappings isconstructed. Indeed, let C be a nonempty closed convex subset of a uniformlyconvex Banach space X whose norm is Gateaux dierentiable and let {Tn} bea family of self-mappings on C such that the set of all common fixed pointsof {Tn} is nonempty. We construct a sequence {xn} generated by the hybridmethod and also we give the cond...

We discuss renorming properties of the dual of a James tree space JT . We present examples of weakly Lindelöf determined JT such that JT ∗ admits neither strictly convex nor Kadec renorming and of weakly compactly generated JT such that JT ∗ does not admit Kadec renorming although it is strictly convexifiable. The norm of a Banach space is said to be locally uniformly rotund (LUR) if for every ...

In “Is the Frobenius Matrix Norm Induced?”, the authors ask whether the Frobenius and the norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the norm may not be induced. In this note, it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the norm is in fact induced on a particular matrix-v...

A Menger space (a special type of probabilistic metric spaces) is said to be compact if its strong uniformity is compact. We construct, in a natural way, Menger T -metrics on the set of distribution functions, one for each copula T (a special type of continuous t-norms). We show that, on each bounded closed interval of distribution functions, the strong uniformities of all our spaces are induce...

Given the infinitesimal generator A of a C0-semigroup on the Banach space X which satisfies the Kreiss resolvent condition, i.e., there exists an M > 0 such that ‖(sI−A)‖ ≤ M Re(s) for all complex s with positive real part. We show that for general Banach spaces this condition does not give any information on the growth of the associated C0-semigroup. For Hilbert spaces the situation is less dr...

Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the norm topology. (b) If the Banach space admits an equivalent rotund norm, then its weak topology is fragmented by a metric. (c) If the Banach space is weakly ...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...