Search results for "Analisi Matematica"

ZBL MS 63/6 Satco, Bianca-Renata; Turcu, Corneliu-Octavian Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on t…

2013

The authors prove an existence result for a nonlinear integral equation on time scales under weak topology assumption in the target Banach space. In the setting of vector valued functions on time scales they consider the Henstock-Kurzweil-Pettis $\Delta$-integral which is a kind of Henstock integral recently introduced by Cichon, M. [Commun. Math. Anal. 11 (2011), no. 1, 94�110]. In this framework they show the existence of weakly continuous solutions for an integral equation x(t)= f(t, x(t))+ (HKP)\int_0^t g(t,s,x(s)) \Delta s governed by the sum of two operators: a continuous operator and an integral one. The main tool to get the solutions is a generalization of Krasnosel'skii fixed point…

THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL

2022

We compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one.

HENSTOCK- AND PERRON-TYPE INTEGRAL ON A COMPACT ZERO-DIMENSIONAL METRIC SPACE

2011

MR3136189 Reviewed Merghadi, F.; Godet-Thobie, C. Common fixed point theorems under contractive conditions of integral type in symmetric spaces. Demo…

2014

The problem of establishing the existence of fixed points for mappings satisfying weak contractive conditions in metric spaces has been widely investigated in the last few decades. More recently, many papers have been published extending this study to various metric contexts. In the paper under review, the authors prove some common fixed point results for symmetric (or semi-metric) spaces. They use implicit contractive conditions of integral type for mappings satisfying weak compatibility or occasionally weak compatibility hypotheses. Some examples are given to illustrate the obtained results.

Partial inner product spaces: Theory and Applications

2010

Partial Inner Product (PIP) Spaces are ubiquitous, e.g. Rigged Hilbert spaces, chains of Hilbert or Banach spaces (such as the Lebesgue spaces Lp over the real line), etc. In fact, most functional spaces used in (quantum) physics and in signal processing are of this type. The book contains a systematic analysis of PIP spaces and operators defined on them. Numerous examples are described in detail and a large bibliography is provided. Finally, the last chapters cover the many applications of PIP spaces in physics and in signal/image processing, respectively. As such, the book will be useful both for researchers in mathematics and practitioners of these disciplines.

AN ADDENDUM TO: A COMMON FIXED POINT THEOREM IN INTUITIONISTIC FUZZY METRIC SPACE USING SUBCOMPATIBLE MAPS"

2012

The aim of this note is to point out a fallacy in the proof of Theorem 3.1 contained in the recent paper ( Int. J. Contemp. Math. Sci. 5 (2010), 2699-2707) proved in intuitionistic fuzzy metric spaces employing the newly introduced notion of sub-compatible pair of mappings wherein our claim is also substantiated with the aid of an appropriate example. We also rectify the erratic theorem in two ways.

MR3785684 Reviewed Liu, Ai Fang(PRC-NAA); Li, Peng Tong(PRC-NAA) K-fusion frames and the corresponding generators for unitary systems. (English summa…

2018

Given an operator K∈B(H), in this paper the authors introduce K-fusion frames as a generalization of fusion frames, defined as a sequence {Wi} of closed subspaces of the Hilbert space H. For K=1, this becomes a fusion frame. They prove some properties of K-fusion frames, based on considering the operator K and the frame operators. In the last section, for a unitary system U, the authors define a K-fusion frame generator in a way similar to the frame vectors for unitary systems. Some properties and characterization theorems are derived for operators in the generalized local commutant of U.

AN APPLICATION OF A FIXED POINT THEOREM FOR NONEXPANSIVE OPERATORS

2014

Abstract. In this note, we present an application of a recent xed point theorem by Ricceri to a two-point boundary value problem. KeyWords and Phrases: Fixed point, nonexpansive operator, two-point boundary value problem. 2010 Mathematics Subject Classi cation: 34K10, 47H09, 47H10.

MR2666982 Heo, Jaeseong; Hong, Jang Pyo; Ji, Un Cig On KSGNS representations on Krein C∗-modules. J. Math. Phys. 51 (2010), no. 5, 053504, 13 pp. (Re…

2011

MR2657294 (2011h:28021) Bensimhoun, Michael Change of variable theorems for the KH integral. Real Anal. Exchange 35 (2010), no. 1, 167–194. (Reviewer…

2010

From Reviews: 0 MR2657294 (2011h:28021) Bensimhoun, Michael(IL-HEBR) Change of variable theorems for the KH integral. (English summary) Real Anal. Exchange 35 (2010), no. 1, 167–194. 28B05 (26A42 46G10) PDF Clipboard Journal Article Make Link Let $({\scr E},{\scr F}, {\scr G})$(E,F,G) be a Banach triple and let $f\colon [a,b] \subset \overline{\Bbb R} \rightarrow {\scr E}$f:[a,b]⊂R−−→E, $\varphi \colon [a,b] \rightarrow {\scr F}$φ:[a,b]→F and $\psi\colon [c,d] \subset \overline{\Bbb R} \rightarrow [a,b]$ψ:[c,d]⊂R−−→[a,b] be given. The problem of change of variables in an integral consists in finding the best conditions under which the equality $$ \int_c^d f \circ \psi \cdot d(\varphi \circ …