Relevant bibliographies by topics / Uniform Lipschitz mapping

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Uniform Lipschitz mapping'

Author: Grafiati
Published: 5 June 2025
Last updated: 16 July 2025

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Journal articles on the topic "Uniform Lipschitz mapping"

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Veysel, Nezir, and Güven Aysun. "On Cesàro Difference Sequence Spaces, their Köthe-Toeplitz Duals and Coefficient Estimate of Fixed Point Property for Uniform Lipschitz Mappings." Journal of Scientific and Engineering Research 8, no. 10 (2021): 141–47. https://doi.org/10.5281/zenodo.10618835.

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<strong>Abstract</strong> In 1970, Ces&agrave;ro Sequence Spaces was introduced by Shiue. In 1981, Kızmaz defined difference sequence spaces for , &nbsp;and . Then, in 1983, Orhan introduced Ces&agrave;ro Difference Sequence Spaces. In this study, first we discuss the fixed point property for these spaces. Then, we recall that Dowling, Lennard and Turett showed that if a Banach space contains an isomorphic copy of , then it fails the fixed point property for uniform Lipschitz mappings. So we worked on a right shift mapping defined on a closed, bounded and convex subset of a K&ouml;the-Toeplitz Dual of a Ces&agrave;ro Difference Sequence Space so that the right shift mapping can be a uniform Lipschitz mapping. Thus, we investigate an upper bound estimate for the right shift mapping to be uniformly Lipschitz failing the fixed point property on a class of closed, bounded and convex subsets in those spaces.
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Miao, Xin-He, and Jein-Shan Chen. "Lipschitz Continuity of the Solution Mapping of Symmetric Cone Complementarity Problems." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/130682.

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This paper investigates the Lipschitz continuity of the solution mapping of symmetric cone (linear or nonlinear) complementarity problems (SCLCP or SCCP, resp.) over Euclidean Jordan algebras. We show that if the transformation has uniform CartesianP-property, then the solution mapping of the SCCP is Lipschitz continuous. Moreover, we establish that the monotonicity of mapping and the Lipschitz continuity of solutions of the SCLCP imply ultraP-property, which is a concept recently developed for linear transformations on Euclidean Jordan algebra. For a Lyapunov transformation, we prove that the strong monotonicity property, the ultraP-property, the CartesianP-property, and the Lipschitz continuity of the solutions are all equivalent to each other.
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Maleva, Olga. "On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane." Abstract and Applied Analysis 2005, no. 5 (2005): 543–62. http://dx.doi.org/10.1155/aaa.2005.543.

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We give a sharp estimate on the cardinality of point preimages of a uniform co-Lipschitz mapping on the plane. We also give a necessary and sufficient condition for a ball noncollapsing Lipschitz function to have a point with infinite preimage.
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Tan, Jianguo, Hongli Wang, and Yongfeng Guo. "Existence and Uniqueness of Solutions to Neutral Stochastic Functional Differential Equations with Poisson Jumps." Abstract and Applied Analysis 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/371239.

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A class of neutral stochastic functional differential equations with Poisson jumps (NSFDEwPJs),d[x(t)-G(xt)]=f(xt,t)dt+g(xt,t)dW(t)+h(xt,t)dN(t),t∈[t0,T], with initial valuext0=ξ={ξ(θ):-τ≤θ≤0}, is investigated. First, we consider the existence and uniqueness of solutions to NSFDEwPJs under the uniform Lipschitz condition, the linear growth condition, and the contractive mapping. Then, the uniform Lipschitz condition is replaced by the local Lipschitz condition, and the existence and uniqueness theorem for NSFDEwPJs is also derived.
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Zhukovskaya, Zukhra T., та Sergey E. Zhukovskiy. "On the existence of a continuously differentiable solution to the Cauchy problem for implicit differential equations". Russian Universities Reports. Mathematics, № 128 (2019): 376–83. http://dx.doi.org/10.20310/2686-9667-2019-24-128-376-383.

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We study the question of the existence of a solution to the Cauchy problem for a differential equation unsolved with respect to the derivative of the unknown function. Differential equations generated by twice continuously differentiable mappings are considered. We give an example showing that the assumption of regularity of the mapping at each point of the domain is not enough for the solvability of the Cauchy problem. The concept of uniform regularity for the considered mappings is introduced. It is shown that the assumption of uniform regularity is sufficient for the local solvability of the Cauchy problem for any initial point in the class of continuously differentiable functions. It is shown that if the mapping defining the differential equation is majorized by mappings of a special form, then the solution of the Cauchy problem under consideration can be extended to a given time interval. The case of the Lipschitz dependence of the mapping defining the equation on the phase variable is considered. For this case, estimates of non-extendable solutions of the Cauchy problem are found. The results are compared with known ones. It is shown that under the assumptions of the proved existence theorem, the uniqueness of a solution may fail to hold. We provide examples llustrating the importance of the assumption of uniform regularity.
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Merchela, Wassim. "On stability of solutions of integral equations in the class of measurable functions." Russian Universities Reports. Mathematics, no. 133 (2021): 44–54. http://dx.doi.org/10.20310/2686-9667-2021-26-133-44-54.

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Consider the equation G(x)=(y,) ̃ where the mapping G acts from a metric space X into a space Y, on which a distance is defined, y ̃ ∈ Y. The metric in X and the distance in Y can take on the value ∞, the distance satisfies only one property of a metric: the distance between y,z ∈Y is zero if and only if y= z. For mappings X → Y the notions of sets of covering, Lipschitz property, and closedness are defined. In these terms, the assertion is obtained about the stability in the metric space X of solutions of the considered equation to changes of the mapping G and the element y ̃. This assertion is applied to the study of the integral equation f(t,∫_0^1▒K (t,s)x(s)ds,x(t))= y ̃(t),t ∈[0,1], with respect to an unknown Lebesgue measurable function x: [0,1] ∈R. Sufficient conditions are obtained for the stability of solutions (in the space of measurable functions with the topology of uniform convergence) to changes of the functions f,K,(y.) ̃
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Tuncer, Necibe, and Anotida Madzvamuse. "Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces." Communications in Computational Physics 21, no. 3 (2017): 718–47. http://dx.doi.org/10.4208/cicp.oa-2016-0029.

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AbstractThe focus of this article is to present the projected finite element method for solving systems of reaction-diffusion equations on evolving closed spheroidal surfaces with applications to pattern formation. The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discretization which is “logically” rectangular. Furthermore, the surface is not approximated but described exactly through the projection. The surface evolution law is incorporated into the projection operator resulting in a time-dependent operator. The time-dependent projection operator is composed of the radial projection with a Lipschitz continuous mapping. The projection operator is used to generate the surface mesh whose connectivity remains constant during the evolution of the surface. To illustrate the methodology several numerical experiments are exhibited for different surface evolution laws such as uniform isotropic (linear, logistic and exponential), anisotropic, and concentration-driven. This numerical methodology allows us to study new reaction-kinetics that only give rise to patterning in the presence of surface evolution such as theactivator-activatorandshort-range inhibition; long-range activation.
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Shukla, Rahul, and Andrzej Wiśnicki. "Iterative methods for monotone nonexpansive mappings in uniformly convex spaces." Advances in Nonlinear Analysis 10, no. 1 (2021): 1061–70. http://dx.doi.org/10.1515/anona-2020-0170.

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Abstract We show the nonlinear ergodic theorem for monotone 1-Lipschitz mappings in uniformly convex spaces: if C is a bounded closed convex subset of an ordered uniformly convex space (X, ∣·∣, ⪯), T:C → C a monotone 1-Lipschitz mapping and x ⪯ T(x), then the sequence of averages 1 n ∑ i = 0 n − 1 T i ( x ) $ \frac{1}{n}\sum\nolimits_{i=0}^{n-1}T^{i}(x) $ converges weakly to a fixed point of T. As a consequence, it is shown that the sequence of Picard’s iteration {T n (x)} also converges weakly to a fixed point of T. The results are new even in a Hilbert space. The Krasnosel’skiĭ-Mann and the Halpern iteration schemes are studied as well.
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Zhang, Jichao, Lingxin Bao, and Lili Su. "On Fixed Point Property under Lipschitz and Uniform Embeddings." Journal of Function Spaces 2018 (October 21, 2018): 1–6. http://dx.doi.org/10.1155/2018/4758546.

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We first present a generalization of ω⁎-Gâteaux differentiability theorems of Lipschitz mappings from open sets to those closed convex sets admitting nonsupport points and then show that every nonempty bounded closed convex subset of a Banach space has the fixed point property for isometries if it Lipschitz embeds into a super reflexive space. With the application of Baudier-Lancien-Schlumprecht’s theorem, we finally show that every nonempty bounded closed convex subset of a Banach space has the fixed point property for continuous affine mappings if it uniformly embeds into the Tsirelson space T⁎.
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Peperko, Aljoša. "Uniform Boundedness Principle for Nonlinear Operators on Cones of Functions." Journal of Function Spaces 2018 (2018): 1–5. http://dx.doi.org/10.1155/2018/6783748.

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We prove a uniform boundedness principle for the Lipschitz seminorm of continuous, monotone, positively homogeneous, and subadditive mappings on suitable cones of functions. The result is applicable to several classes of classically nonlinear operators.
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Dissertations / Theses on the topic "Uniform Lipschitz mapping"

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Pernecká, Eva. "Analýza v Banachových prostorech." Doctoral thesis, 2014. http://www.nusl.cz/ntk/nusl-332331.

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The thesis consists of two papers and one preprint. The two papers are de- voted to the approximation properties of Lipschitz-free spaces. In the first pa- per we prove that the Lipschitz-free space over a doubling metric space has the bounded approximation property. In particular, the Lipschitz-free space over a closed subset of Rn has the bounded approximation property. We also show that the Lipschitz-free spaces over ℓ1 and over ℓn 1 admit a monotone finite-dimensional Schauder decomposition. In the second paper we improve this work and obtain even a Schauder basis in the Lipschitz-free spaces over ℓ1 and ℓn 1 . The topic of the preprint is rigidity of ℓ∞ and ℓn ∞ with respect to uniformly differentiable map- pings. Our main result is a non-linear analogy of the classical result on rigidity of ℓ∞ with respect to non-weakly compact linear operators by Rosenthal, and it generalises the theorem on non-complementability of c0 in ℓ∞ due to Phillips. 1
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Book chapters on the topic "Uniform Lipschitz mapping"

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Zhang, Jian, Yaping Yu, and Yanli Liu. "The Convergence Theorems of Fixed Points for Nearly Uniformly L-Lipschitz Mappings." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34041-3_39.

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