Search results for " Opera"
showing 10 items of 3606 documents
MR2449047 (2009j:47108) Chermisi, Milena; Martellotti, Anna Fixed point theorems for middle point linear operators in $L^1$. Fixed Point Theory Appl.…
2009
In the paper under review the notion of middle point operator is introduced. The authors prove that for a given nonempty, bounded, $\rho$-closed, convex subset K of L1(μ), where $\rho$ is the metric of the convergence locally in measure, if T from (K, $\rho$) to(K, $\rho$) is a continuous, $\rho$-nonexpansive, middle point linear operator, then T has at least one fixed point in K. To prove the theorem they use results of A. V. Bukhvalov [in Operator theory in function spaces and Banach lattices, 95–112, Birkh¨auser, Basel, 1995; MR1322501 (95m:46123)] and M. Furi and A. Vignoli [Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 48 (1970), 195–198; MR0279792 (43 #5513)]. Then they …
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.
A note on boundary conditions for nonlinear operators
2008
We investigate boundary conditions for strict-$\psi$-contractive and $\psi$-condensing operators. We derive results on the existence of eigenvectors with positive and negative eigenvalues and we obtain fixed point theorems for classes of noncompact opera\-tors.
Eigenvectors of k-psi-contractive wedge operators
2008
We present new boundary conditions under which the fixed point index of a strict-$\psi$-contractive wedge operator is zero. Then we investigate eigenvalues and corresponding eigenvectors of k-$\psi$-contractive wedge operators.
MR2819034 Castillo, René Erlín The Nemytskii operator on bounded p-variation in the mean spaces. Mat. Enseñ. Univ. (N. S.) 19 (2011), no. 1, 31–41. (…
2012
The author introduces the notion of bounded $p$-variation in the sense of $L_p$-norm. Precisely: Let $f \in L_p[0,2\pi]$ with $1<p<\infty$. Let $P: 0=t_0 <t_1< \cdots <t_n=2\pi$ be a partion of $[0,2\pi]$ if $$V_p^m(f,T) = \sup \{\sum_{k=1} ^{n}\int_T\frac{|f(x+t_k)-f(x+t_{k-1})|^p)}{|t_k-t_{k-1}|^{p-1}}\}< \infty,$$ where the supremum is taken over all partitions $P$ of $[0,2\pi]$ and $T=\mathbb{R}/2\pi \mathbb{Z}$, then $f$ is said to be of bounded $p$-variation in the mean. The author obtains a Riesz type result for functions of bounded $p$-variation in the mean and gives some properties for functions of bounded $p$-variation by using the Nemytskii operator.
Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems
2020
We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter λ > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution.
Perturbations of polaroid type operators on Banach spaces and Applications
2011
We study the permanence of polaroid type conditions under perturbations
Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that
2016
Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity between operators and explore to what extent they preserve spectral properties. Then we study quasi-Hermitian operators, bounded or not, that is, operators that are quasisimilar to their adjoint and we discuss their application in pseudo-Hermitian quantum mechanics. Finally, we extend the analysis to operators in a partial inner product space (PIP-space), in particular the scale of Hilbert spaces generated by a single unbounded metric operator.
Some remarks on quasi-Hermitian operators
2014
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator.Whereas those metric operators are in general assumed to be bounded, we analyze the structure generated by unbounded metric operators in a Hilbert space. Following our previous work, we introduce several generalizations of the notion of similarity between operators. Then we explore systematically the various types of quasi-Hermitian operators, bounded or not. Finally, we discuss their application in the so-called pseudo-Hermitian quantum mechanics.