Inomjon Ganiev, Farrukh Mukhamedov, Dilmurad Bekbae
In the present paper we study majorizable operators acting on Banach-Kantorovich $L_p$-lattices, constructed by a measure $m$ with values in the ring of all measurable functions. Then using methods of measurable bundles of Banach-Kantorovich lattices, we prove the strong "zero-two" law for positive contractions of the Banach-Kantorovich $L_p$-lattices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We present versions of ergodic theorems for $L_1$--$L_\infty$ contractions in Banach--Kantorovich $L_p$-lattices associated with the Maharam measure taking values in the algebra of measurable functions.
In the present paper we prove the "zero-two" law for positive contractions of lattices $L^p(\nabla,μ)$ of Banach-Kantorovich, constructed by the measure $μ$ with values in the ring of all measurable functions.
In the present paper we prove Besocovich weighted ergodic theorem for positive contractions acting on Orlich-Kantorovich space. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices.
In the present paper we prove weighted ergodic theorems and multiparameter weighted ergodic theorems for positive contractions acting on $L_p(\hat{\nabla},\hatμ)$. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices.
In the present paper we investigate Banach--Kantorovich algebras over faithful solid subalgebras of algebras measurable functions. We prove that any Banach--Kantorovich algebra over faithful solid subalgebras of algebra measurable functions represented as a measurable bundle of Banach algebras with vector-valued lifting. We apply such representation to the spectrum of elements Banach--Kantorovich algebras.
We show that every dominated linear operator from an Banach-Kantorovich space over atomless Dedekind complete vector lattice to a sequence Banach lattice $l_p(Γ)$ or $c_0(Γ)$ is narrow. As a conse- quence, we obtain that an atomless Banach lattice cannot have a finite dimensional decomposition of a certain kind. Finally we show that if a linear dominated operator T from lattice-normed space V to Banach- Kantorovich space W is order narrow then the same is its exact dominant $\ls T\rs$.
Approximation by Kantorovich-type operators in general Banach spaces
本文在一般巴拿赫格中研究线性 Kantorovich 型采样算子的逼近性质，在 Steklov 平均算子一致有界假设下建立相关估计，其框架无需空间平移不变，扩展了仅针对$L_p$空间的相关估计。
The aim of this article is to extend results of M.~Popov and second named author about orthogonally additive narrow operators on vector lattices. The main object of our investigations are an orthogonally additive narrow operators between lattice-normed spaces. We prove that every $C$-compact laterally-to-norm continuous orthogonally additive operator from a Banach-Kantorovich space $V$ to a Banach lattice $Y$ is narrow. We also show that every dominated Uryson operator from Banach-Kantorovich space over an atomless Dedekind complete vector lattice $E$ to a sequence Banach lattice $\ell_p(Γ)$ o…
In this paper, we improve and generalize the operator versions of Kantorovich and Wielandt inequalities for positive linear maps on Hilbert space. Our results are more extensive and precise than many previous results due to Fu and He [Linear Multilinear Algebra, doi: 10. 1080/03081087. 2014. 880432.] and Zhang [Banach J. Math. Anal., 9 (2015), no. 1, 166-172.].
Our aim in this paper is to present a new type of the modular space. This space contains the classical modular space. There are some mappings that do not have contractive condition in the usual modular space but become contraction in this new space.
In this paper we introduce the notion of a Caristi-Banach type $\mathcal{Z}_{R}^{b}$- contraction in the framework of $b$- metric space endowed with a transitive relation that combine the ideas of Caristi type contraction and Banach contraction with a help of simulation function. We present an example to clarify the statement of the given result.
In this paper, we present the generalization of B-contraction and C-contraction due to Sehgal and Hicks respectively. We also study some properties of C-contraction in probabilistic metric space.
In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.
We introduce the concept of weak L-P property for a pair of Banach spaces, in the study of extreme contractions. We give examples of pairs of Banach spaces (not) satisfying weak L-P property and apply the concept to compute the exact number of extreme contractions between a particular pair of polygonal Banach spaces. We also study the optimality of our results on the newly introduced weak L-P property for a pair of Banach spaces, by considering appropriate examples.
Let $X$ be a reflexive Banach space such that for any $x \ne 0$ the set $$ \{x^* \in X^*: \text {$\|x^*\|=1$ and $x^*(x)=\|x\|$}\} $$ is compact. We prove that any unrestricted product of of a finite number of $(W)$ contractions on $X$ converges weakly.
Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, introduced in [Berinde, V., {\it Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces}, Carpathian J. Math. {\bf 35} (2019), no. 3, 277-288.], we introduce the class of enriched Chatterjea contractions and prove general fixed point theorems for such contractions in the setting of a Banach space. Examples to illustrate the richness of the new class of contractions and the relationship between enriched Banach contractions, enriched Kannan contractions an…
We introduce a large class of mappings, called enriched contractions, which includes, amongst many other contractive type mappings, the Picard-Banach contractions and some nonexpansive mappings. We show that any enriched contraction has a unique fixed point and that this fixed point can be approximated by means of an appropriate Kransnoselskij iterative scheme. Several important results in fixed point theory are shown to be corollaries or consequences of the main results in this paper. We also study the fixed points of local enriched contractions, asymptotic enriched contractions and Maia type…
We introduce a large class of contractive mappings, called Suzuki Berinde type contraction. We show that any Suzuki Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mapping is also obtained. These results unify, generalize and complement various known comparable results in the literature.
In this paper, by using admissible sets, we give some fixed point results for orbitally contractions which diminish the radius of invariant convex subsets and orbits. Furthermore, a characterization of the weak normal structure by the fixed point property associated with this class of mappings is established.
A Restatement of Fixed Point Existence: From Banach to Singh Contractions
本文重述二阶边值问题的存在唯一性结果，引入Singh压缩条件（允许T^p满足条件），展示广义压缩在Banach压缩原理失效时的应用。
In this short work we consider nonlinear equation in Banach space $x = A(x)$. We combine classical Newton method with Vietoris method to propose new more general method. Under rather general conditions about the noise we investigate local convergence of the method.
In this paper, we introduce two new types of enriched contractions, viz., enriched $\mathcal{A}$-contraction and enriched $\mathcal{A}'$-contraction. Then we obtain fixed points of mappings satisfying such contractions using the fixed point property of the average operator of the mappings. Further, we study the well-posedness and limit shadowing property of the fixed point problem involving the contractions, and give some examples to validate the results proved. We frame an open question related to the existence of a fixed point of such contractions. We also show that Berinde and Păcurar's rec…
Convergence of C-Class Enriched Hardy-Rogers Contractions in some Banach Spaces
本文利用C类函数推广富集Hardy-Rogers压缩映射，在Banach空间中通过迭代格式建立唯一不动点及公共不动点的收敛性，推广了近期相关结果。
Let $X$ be a complex Banach space and let $J:X \to X^*$ be a duality section on $X$ (i.e. $\langle x,J(x)\rangle=\|J(x)\|\|x\|=\|J(x)\|^2=\|x\|^2$). For any unit vector $x$ and any ($C_0$) contraction semigroup $T=\{e^{tA}:t \geq 0\}$, Goldstein proved that if $X$ is a Hilbert space and if $|\langle T(t) x,J(x)\rangle| \to 1 $ as $t \to \infty$, then $x$ is an eigenvector of $A$ corresponding to a purely imaginary eigenvalue. In this article, we prove the similar result holds if $X$ is a strictly convex complex Banach space.
Extreme contractions on finite-dimensional Banach spaces
本研究聚焦有限维多面体Banach空间的极端压缩算子，受Krein-Milman定理启发，证明二维定义域下及ℓ_∞^n(ℂ)到ℓ_1^n(ℂ)的算子空间中，秩一范一算子可表为秩一极端压缩算子的凸组合，并给出该类算子的几何刻画。
Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle
该研究提出新型自映射PA-压缩（路径平均压缩），证明完备度量空间上连续PA-压缩有唯一不动点且Picard迭代收敛，严格推广Banach压缩原理，验证其与多种经典压缩映射独立，可捕捉逐点压缩失效时的长期压缩行为。
Extreme contractions on finite-dimensional polygonal Banach spaces
本文研究有限维多边形Banach空间之间极端压缩算子的范数可达性，证明其范数在单位球n个线性无关极端点上可达，并引入L-P性质刻画严格凸Banach空间与Hilbert空间的关系。
On extreme contractions between real Banach spaces
本文通过引入相容点对（CPP）和 μ-相容点对（μ-CPP）的新几何概念，首次完全刻画了二维严格凸光滑实 Banach 空间之间的极端压缩算子，并应用于具体空间及无穷维情形，进而用 CPP 刻画了实 Hilbert 空间。
Cyclic p-$ϕ$-contraction mappings
本文提出循环p-φ压缩映射的概念，并研究其在不同空间中的固定点存在性和唯一性。
Characterization of extreme contractions through $k-$smoothness of operators
该研究利用算子$k$-光滑性刻画有限维多面体Banach空间间的极端压缩算子，探讨弱L-P性质并给出其满足的充分条件，还显式计算了特殊Banach空间中极端压缩算子的数量，改进推广了已有结果。
A Kantorovich-type variant of Grünwald Interpolation Operators
本文提出基于Chebyshev节点的Grünwald插值算子序列，扩展到L^p空间，并通过连续性和Kantorovich定理证明了在多种Banach函数空间中的收敛性。
Perimetric contraction on quadrilaterals and related fixed point results
本文提出Banach、Kannan、Chatterjea三类收缩的四点类似形式，推导其在完备度量空间中存在不动点的充分条件，证明经典Banach收缩原理为其特例，并给出非平凡示例验证理论结果。
A converse of the Banach contraction principle for partial metric spaces and the continuum hypothesis
研究将 Banach 压缩原理的 Bessaga 逆命题推广至偏度量空间，并证明其相应版本与连续统假设等价。
It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present paper represents the development of some fixed point results regarding sequences of contractions in the setting of cone metric spaces over Banach algebras. Furthermore, some examples are given in order to strengthen our new concepts. Also, based on the powerful notion of a cone metric space over a Banach algebra, we present important applications to systems …
We augment the dimension of the Euclidean space by one and the Picard iteration of a contraction by a simple iteration on the real line such that the resulting iteration becomes monotone increasing and bounded with respect to the order defined by the Lorentz cone of the augmented space. This provides a different way of showing the convergence of the Picard iteration of a contraction, exhibiting the strong relationship between the Banach fixed point principle and the ordering structure of the Euclidean space ordered by the Lorentz cone.
The aim of this note is to introduce the space D_{U}(V,W) of the dominated Uryson operators on lattice-normed spaces. We prove an "Up-and-down" type theorem for a positive abstract Uryson operator defined on a vector lattice and taking values in a Dedekind complete vector lattice. This result we apply to prove the decomposability of the lattice valued norm of the space D_{U}(V,W) of all dominated Uryson operators. We obtain that, for a lattice-normed space V and a Banach-Kantorovich space W the space D_{U}(V,W) is also a Banach-Kantorovich space. We prove that under some mild conditions, a dom…
Geodesic contraction in vector-valued differential equations is readily verified by linearized operators which are uniformly negative-definite in the Riemannian metric. In the infinite-dimensional setting, however, such analysis is generally restricted to norm-contracting systems. We develop a generalization of geodesic contraction rates to Banach spaces using a smoothly-weighted semi-inner product structure on tangent spaces. We show that negative contraction rates in bijectively weighted spaces imply asymptotic norm-contraction, and apply recent results on asymptotic contractions in Banach s…
In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear operator, accepted in Journal of Mathematical Analysis and Applications}]. We further study the extreme contractions on various types of finite-dimensional Banach spaces, namely Euclidean spaces, and strictly convex spaces. In particular, we give an elementary alternative proof of the well-known characterization of extreme contractions on a Hilbert space, that works…
For any complex Banach space $X$, let $J$ denote the duality mapping of $X$. For any unit vector $x$ in $X$ and any ($C_0$) contraction semigroup $(T_t)_{t>0}$ on $X$, Baillon and Guerre-Delabriere proved that if $X$ is a smooth reflexive Banach space and if there is $x^* \in J(x)$ such that $|\langle T(t) \, x,J(x)\rangle| \to 1 $ as $t \to \infty$, then there is a unit vector $y\in X$ which is an eigenvector of the generator $A$ of $(T_t)_{t>0}$ associated with a purely imaginary eigenvalue. They asked whether this result is still true if $X$ is replaced by $c_o$. In this article, we show th…
The aim of this article is to extend results of Maslyuchenko O., Mykhaylyuk V. Popov M. about narrow operators on vector lattices. We give a new definition of a narrow operator where a vector lattice as the domain space of a narrow operator is replaced with a lattice-normed space. We prove that every GAM-compact (bo)-norm continuous linear operator from a Banach-Kantorovich space V to a Banach lattice Y is narrow. Then we show that, under some mild conditions, a continuous dominated operator is narrow if and only if its exact dominant is narrow.
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting an elementary proof for a known fixed point result. Some applications are also considered.
Typical properties of positive contractions and the invariant subspace problem
本文研究了典型正收缩在不同拓扑下的不变子空间性质，并证明了其在某些条件下不满足Abramovich, Aliprantis和Burkinshaw准则。
On the Picard-Lindelöf Argument and the Banach-Caccioppoli Contraction Mapping Principle
本文通过改进收缩映射原理，实现了对皮卡-林德勒夫定理中收敛速率的精确恢复。
Contraction rates of time-varying maps induced by dynamical systems illuminate a wide range of asymptotic properties with applications in stability analysis and control theory. In finite-dimensional smoothly varying inner-product spaces such as $\mathbb{R}^n$ and $\mathbb{C}^n$ with Riemannian metrics, contraction rates can be estimated by upper-bounding the real numerical range of the vector field's Jacobian. However, vector spaces with norms other than $L^2$ commonly arise in the stability analysis of infinite-dimensional systems such as those arising from partial differential equations and …
A dilation theoretic approach to Banach spaces
本文通过膨胀理论研究巴拿赫空间，证明了严格压缩可膨胀为等距映射等条件是空间成为希尔伯特空间的充要条件，并刻画了非希尔伯特空间中的等距膨胀及算子范数达到集等性质。
A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric spaces that fulfill an extra regularity property. The stability of fixed points is also investigated in this setting. As applications, fixed point results are presented for several important generalizations of metric spaces.
In this paper we collect results concerning the {operator-norm} convergent {Trotter} product formula for two semigroups $\{\e^{- t A}\}_{t\geq 0}$, $\{\e^{- t B}\}_{t\geq 0}$, with densely defined generators $A$ and $B$ in a {Banach} space. Although the {strong} convergence in Banach space for contraction semigroups is known since the seminal paper by Trotter (1959), which after more than three decades was extended to convergence in the {operator-norm} topology in {Hilbert} spaces by Rogava (1993), the {operator-norm} convergence in a {Banach} space was established only in (2001).
We study the generalization of $m$-isometries and $m$-contractions (for positive integers $m$) to what we call $a$-isometries and $a$-contractions for positive real numbers $a$. We show that any Hilbert space operator, satisfying an inequality of certain class (in hereditary form), is similar to $a$-contractions. This result is based on some Banach algebras techniques and is an improvement of a recent result by the last two authors. We also prove that any $a$-contraction $T$ is a $b$-contraction, if $b<a$ and one imposes an additional condition on the growth of the norms of $T^n x$, where $x$ …
Further results on $p$-adic semigroup of contractions
本文在超度量Banach空间上，给出了算子$A$的预解式条件，使得对所有自然数$m$，$\\\\|A^m\\\\|\leq 1$，即$A$为压缩算子。
The motive behind this manuscript is to set up the existence and uniqueness of a positive solution for a fractional thermostat model for certain values of the parameter $λ>0$. We accomplish sufficient conditions for the existence of a positive solution to the model, and afterwards formulate a non-trivial example to authenticate the grounds of our obtained results. Our findings are based on certain fixed point results of contractions depending on couple of altering distance functions $ϕ$ and $ψ$ in the setting of Banach spaces that are discussed in this sequel.
The following theorem is essentially due to L.~Kantorovich and B. Vulikh and it describes one of the most important classes of Banach lattices between which each continuous operator is regular. {\bf Theorem 1.1.} {\sl Let $E$ be an arbitrary L-space and $F$ be an arbitrary Banach lattice with Levi norm. Then ${\cal L}(E,F)={\cal L}^r(E,F),\ (\star) $ that is, every continuous operator from $E$ to $F$ is regular.} In spite of the importance of this theorem it has not yet been determined to what extent the Levi condition is essential for the validity of equality $(\star)$. Our main aim in this w…
Free Banach lattices over pre-ordered Banach spaces
研究预序巴拿赫空间在给定凸性类型下的自由巴拿赫格，确定正收缩的单射性和闭范围条件，以及其作为函数格的实现。
The purpose of the present notes is to examine the following issues related to the the Chernoff estimate: (1) For contractions on a Banach space we modify the $\sqrt{n}$-estimate and apply it in the proof of the Chernoff product formula for $C_0$-semigroups in the \textit{strong} operator topology. (2) We use the idea of a {probabilistic} approach, proving the Chernoff estimate in the strong operator topology, to uplift it to the \textit{operator-norm} estimate for \textit{quasi-sectorial} contraction semigroups. (3) The operator-norm Chernoff estimate is applied to {quasi-sectorial} contracti…
We prove that, in a large class of Banach lattices, the fixed space of each commuting family of positive linear contractions is a lattice subspace. As consequences, new cyclicity results for the peripheral point spectra of positive operators and semigroups are derived; we also pose an open problem that naturally occurs in this context. Finally, a variety of counterexamples is presented to point out some limits of our results.
In this paper, we show that several extension of Banach contraction principle, can be easily derived from the Caristi's theorem is one of the useful generalization of Banach contraction principle in the setting of the complete metric spaces. Moreover, some partial answers to some known open problems are given via Caristi's corollaries. Finally, existence of bounded solutions of a functional equation is studied to support our results.
By iterative techniques,we present two fixed point theorems, whose modular formulations are relatively close to the Banach's fixed point theorem in the normed spaces.The first result concerns the fixed point of the strongly contraction mappings.The second result deals with the fixed point of the strict contraction mappings where the modular satisfies the delta-condition. For the nonexpansive mappings,where the modular satisfies the regular growth condition,we present a fixed point theorem of the Shauder's type,without boundedness condition on the domain of theses mappings.
If $X$ is a separable reflexive Banach space, there are several natural Polish topologies on $\mathcal{B}(X)$, the set of contraction operators on $X$ (none of which being clearly ``more natural'' than the others), and hence several a priori different notions of genericity -- in the Baire category sense -- for properties of contraction operators. So it makes sense to investigate to which extent the generic properties, i.e. the comeager sets, really depend on the chosen topology on $\mathcal{B}(X)$. In this paper, we focus on $\ell_p\,$-$\,$spaces, $1<p\neq 2<\infty$. We show that for some pair…
This paper shows the usefulness of Perov's contraction principle, which generalizes Banach's contraction principle to a vector-valued metric, for studying dynamic programming problems in which the discount factor can be stochastic. The discounting condition $β<1$ is replaced by $ρ(B)<1$, where $B$ is an appropriate nonnegative matrix and $ρ$ denotes the spectral radius. Blackwell's sufficient condition is also generalized in this setting. Applications to asset pricing and optimal savings are discussed.
Characterization of k-smoothness of operators defined between infinite-dimensional spaces
该研究刻画了无穷维Hilbert空间间有界线性算子的k-光滑性，在有限与无穷维Banach空间框架下展开研究，给出了若干特定空间上算子k-光滑性的刻画，并将结果应用于极端收缩算子的刻画。
Let $T$ be a bounded linear operator on a Hilbert space $H$ such that \[ α[T^*,T]:=\sum_{n=0}^\infty α_n T^{*n}T^n\ge 0. \] where $α(t)=\sum_{n=0}^\infty α_n t^n$ is a suitable analytic function in the unit disc $\mathbb{D}$ with real coefficients. We prove that if $α(t) = (1-t) \tildeα (t)$, where $\tildeα$ has no roots in $[0,1]$, then $T$ is similar to a contraction. Operators of this type have been investigated by Agler, Müller, Olofsson, Pott and others, however, we treat cases where their techniques do not apply. We write down an explicit Nagy-Foias type model of an operator in this clas…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。