P-normed Space Research Articles

A p-theory of ordered normed spaces

We propose a pair of axioms (O.p.1) and (O.p.2) for 1 ≤ p ≤ ∞ and initiate a study of a (matrix) ordered space with a (matrix) norm, in which the (matrix) norm is related to the (matrix) order. We call such a space a (matricially) order smooth p-normed space. The advantage of studying these spaces over Lp-matricially Riesz normed spaces is that every matricially order smooth ∞-normed space can be order embedded in some C*-algebra. We also study the adjoining of an order unit to a (matricially) order smooth ∞-normed space. As a consequence, we sharpen Arveson’s extension theorem of completely positive maps. Another combination of these axioms yields an order theoretic characterization of the set of real numbers amongst ordered normed linear spaces.

A fixed point approach to almost quartic mappings in quasi fuzzy normed spaces

We will define a notion for a quasi fuzzy p-normed space, then we use the fixed point alternative theorem to establish Hyers–Ulam–Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. Later, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function, control function and the unique quartic mapping which approximates the almost quartic map. Finally, some applications of our results in the stability of quartic mappings from a linear space into a quasi p-norm space will be exhibited.

Recursive CDMA multiuser detection method based on least p-norm state space criterion

Alpha stable distribution is better for modeling impulsive noises than Gaussian distribution in wireless communication system. This class of process has no close form of probability density function and finite second order moments. In general, Wiener filter theory is not meaningful in SαSG environments because the expectations may be unbounded. We proposed a new adaptive recursive least p-norm State space multiuser detection algorithm based on least p-norm of innovation process with infinite variances. The simulation experiments show that the proposed new algorithm is more robust than the conventional state space multi-user detection algorithm.

On pointwise R-subweakly commuting maps and best approximations

The main purpose of this paper is to prove some common fixed point theorems for pointwise R-subweakly commuting maps on non-starshaped domains in p-normed spaces and locally convex topological vector spaces. As applications, invariant approximation results are established. This work provides extension as well as substantial improvement of several results in the existing literature.

Common fixed point, best approximation and generalized f-weak contraction multivalued mapping in p-normed spaces

AbstractWe establish coincidence point and common fixed point results for multi-valued

Robust multiuser detection based on least p-norm state space filtering model

Alpha stable distribution is better for modeling impulsive noises than Gaussian distribution in signal processing. This class of process has no closed form of probability density function and finite second order moments. In general, Wiener filter theory is not meaningful in SaSG environments because the expectations may be unbounded. We proposed a new adaptive recursive least p-norm Kalman filtering algorithm based on least p-norm of innovation process with infinite variances, and a new robust multiuser detection method based on least p-norm Kalman filtering. The simulation experiments show that the proposed new algorithm is more robust than the conventional Kalman filtering multiuser detection algorithm.

Robust Multiuser Detection Method Based on Least p-Norm State Space Criterion

Alpha stable distribution is better for modeling impulsive noises than Gaussian distribution in wireless communication system. This class of process has no close form of probability density function and finite second order moments. In general, Wiener filter theory is not meaningful in ? SG environments because the expectations may be unbounded. We proposed a new adaptive recursive least p-norm State space multiuser detection algorithm based on least p-norm of innovation process with infinite variances. The simulation experiments show that the proposed new algorithm is more robust than the conventional state space multiuser detection algorithm.

GeneralizedI-nonexpansive maps and invariant approximation results inp-normed spaces

We extend the concept of R-subcommuting maps due to Shahzad[17,18] to the case of non-starshaped domain and obtain a common fixed point result for this class of maps on non-starshaped domain in the setup of p-normed spaces. As applications, we establish noncommutative versions of various best approximation results for generalized I-nonexpansive maps on non-starshaped domain. Our results unify and extend that of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Latif, Sahab, Khan and Sessa and Shahzad.

THE ALEKSANDROV PROBLEM FOR UNIT DISTANCE PRESERVING MAPPING

In this paper, one of the Aleksandrov problem was resolved, the proof that a mapping f which preserve unit distance between two real p-normed spaces X and Y is an isometry if Y is a p-strictly convex space and f satisfies locally Lipschitz condition was shown, and a same result in normed spaces was given. In addition, a proof which there doesn’t exist any isometry between some spaces was obtained.

P-Banach Spaces and p-Totally Convex Spaces

We introduce the categories Vec p of p-normed vector spaces, Ban p of p -Banach spaces, AC p of p -absolutely and TC p of p -totally convex spaces (0 < p ≤ 1). It will be shown that TC p (AC p ) is the Eilenberg–Moore category of Ban p (Vec p ). Then congruence relations on TC p (AC p )-spaces are studied. There are many differences between TC p (AC p )-spaces and totally (absolutely) convex spaces (i.e. p = 1) (Pumplun and Rohrl, 1984, 1985), which will become apparent in Section 4.

On the totality of sequences in topological vector spaces

Price and Zink [ Ann. of Math. 82 (1965), 139–145] gave necessary and sufficient conditions for the existence of a multiplier m so that { mφ n } 1 ∞ is total; that is, the linear span is dense in L 2[0, 1], thus answering a question raised by Boas and Pollard [ Bull. Amer. Math. Soc. 54 (1948), 512–522]. Using techniques similar to those of Price and Zink, it is shown that this result can be extended to more general spaces. Indeed, if X is either a separable Fréchet space or a complete separable p-normed space (0 < p ⩽ 1), then the existence of a continuous linear operator A so that { Aφ n } 1 ∞ spans a dense subspace is implied by the existence of a nested, equicontinuous family of commuting projections which in addition has the properties that the union of their ranges is dense and that, for each projection, the projection of the original sequence is total in the projected space. Conversely, in a Banach space, it is shown that if such an operator exists and is 1-1 and scalar, then such a family of projections also exists. Further, it is shown that the above considerations extend the first half of the Price-Zink result to L p [0, 1] (0 < p < ∞) and the other half to L p [0, 1] (1 ⩽ p < ∞).

Functionals F Bilinear over the Product A × B of Two P-Normed Vector Spaces

Functionals F Bilinear over the Product A × B of Two P-Normed Vector Spaces