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Journal articles on the topic 'Uniform Lipschitz mapping'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

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, Cesàro Sequence Spaces was introduced by Shiue. In 1981, Kızmaz defined difference sequence spaces for ,  and . Then, in 1983, Orhan introduced Cesàro 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 Köthe-Toeplitz

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2

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

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3

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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4

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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5

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 Cau

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6

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

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7

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

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8

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

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9

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

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10

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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11

Zhiqun, Xue. "Approximation of fixed points of strongly pseudocontractive mappings in uniformly smooth Banach spaces." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–6. http://dx.doi.org/10.1155/ijmms/2006/46561.

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LetEbe a real uniformly smooth Banach space, andKa nonempty closed convex subset ofE. Assume thatT1+T2:K→Kis a continuous and strongly pseudocontractive mapping, whereT1:K→Kis Lipschitz andT2:K→Khas the bounded range mapping. Then the Ishikawa iterative sequence converges strongly to the unique fixed point ofT1+T2.

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12

ANSARI, QAMRUL HASAN, JAVAD BALOOEE, and SULIMAN AL-HOMIDAN. "An iterative method for variational inclusions and fixed points of total uniformly $L$-Lipschitzian mappings." Carpathian Journal of Mathematics 39, no. 1 (2022): 335–48. http://dx.doi.org/10.37193/cjm.2023.01.24.

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"The characterizations of $m$-relaxed monotone and maximal $m$-relaxed monotone operators are presented and by defining the resolvent operator associated with a maximal $m$-relaxed monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. By using resolvent operator associated with a maximal $m$-relaxed monotone operator, an iterative algorithm is constructed for approximating a common element of the set of fixed points of a total uniformly $L$-Lipschitzian mapping and the set of solutions of a variational inclusion problem involving maximal $

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13

Deng, Lei, and Xieping Ding. "Iterative approximation of Lipschitz strictly pseudocontractive mappings in uniformly smooth Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 24, no. 7 (1995): 981–87. http://dx.doi.org/10.1016/0362-546x(94)00115-x.

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14

Bounekhel, Djalel, Messaoud Bounkhel, and Mostafa Bachar. "Existence Results for Second Order Nonconvex Sweeping Processes in q-Uniformly Convex and 2-Uniformly Smooth Separable Banach Spaces." Symmetry 11, no. 1 (2018): 28. http://dx.doi.org/10.3390/sym11010028.

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We prove an existence result, in the separable Banach spaces setting, for second order differential inclusions of type sweeping process. This type of differential inclusion is defined in terms of normal cones and it covers many dynamic quasi-variational inequalities. In the present paper, we prove in the nonconvex case an existence result of this type of differential inclusions when the separable Banach space is assumed to be q-uniformly convex and 2-uniformly smooth. In our proofs we use recent results on uniformly generalized prox-regular sets. Part of the novelty of the paper is the use of

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15

Randrianantoanina, Beata. "On the structure of level sets of uniform and Lipschitz quotient mappings from $$ \mathbb{R}^n $$ to $$ \mathbb{R} $$." Geometric And Functional Analysis 13, no. 6 (2003): 1329–58. http://dx.doi.org/10.1007/s00039-003-0448-1.

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16

S. Lee, B., and Arif Rafiq. "Strong convergence of an implicit iteration process for a finite family of Lipschitz $\phi -$uniformly pseudocontractive mappings in Banach spaces." Numerical Algebra, Control & Optimization 4, no. 4 (2014): 287–93. http://dx.doi.org/10.3934/naco.2014.4.287.

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17

Perveen, Afshan, Samina Kausar, and Waqas Nazeer. "Strong convergence theorems of common fixed points for a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in Hilbert spaces." Open Journal of Mathematical Analysis 3(2019), no. 1 (2019): 1–6. http://dx.doi.org/10.30538/psrp-oma2019.0027.

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18

Hosoya, Yuhki. "Non-smooth integrability theory." Economic Theory, March 30, 2024. http://dx.doi.org/10.1007/s00199-024-01564-x.

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AbstractWe study a method for calculating the utility function from a candidate of a demand function that is not differentiable, but is locally Lipschitz. Using this method, we obtain two new necessary and sufficient conditions for a candidate of a demand function to be a demand function. The first concerns the Slutsky matrix, and the second is the existence of a concave solution to a partial differential equation. Moreover, we show that the upper semi-continuous weak order that corresponds to the demand function is unique, and that this weak order is represented by our calculated utility func

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19

OI, SHIHO. "A SPHERICAL VERSION OF THE KOWALSKI–SŁODKOWSKI THEOREM AND ITS APPLICATIONS." Journal of the Australian Mathematical Society, December 3, 2020, 1–26. http://dx.doi.org/10.1017/s1446788720000452.

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Abstract Li et al. [‘Weak 2-local isometries on uniform algebras and Lipschitz algebras’, Publ. Mat.63 (2019), 241–264] generalized the Kowalski–Słodkowski theorem by establishing the following spherical variant: let A be a unital complex Banach algebra and let $\Delta : A \to \mathbb {C}$ be a mapping satisfying the following properties: (a) $\Delta $ is 1-homogeneous (that is, $\Delta (\lambda x)=\lambda \Delta (x)$ for all $x \in A$ , $\lambda \in \mathbb C$ ); (b) $\Delta (x)-\Delta (y) \in \mathbb {T}\sigma (x-y), \quad x,y \in A$ . Then $\Delta $ is linear and there exists $\lambda _{0}

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20

"Coefficient Estimate of A Uniform Lipschitz Mapping Failing Fixed Point Property on A Class in The Ko ̈the-Toeplitz Duals for Generalized Cesa`ro Difference Sequence Spaces." Applied Mathematics & Information Sciences 11, no. 2 (2022): 323–29. http://dx.doi.org/10.18576/amis/160220.

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21

Frühwirth, Lorenz, Michael Juhos, and Joscha Prochno. "The large deviation behavior of lacunary sums." Monatshefte für Mathematik, June 24, 2022. http://dx.doi.org/10.1007/s00605-022-01733-x.

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AbstractWe study the large deviation behavior of lacunary sums $$(S_n/n)_{n\in {\mathbb {N}}}$$ ( S n / n ) n ∈ N with $$S_n:= \sum _{k=1}^nf(a_kU)$$ S n : = ∑ k = 1 n f ( a k U ) , $$n\in {\mathbb {N}}$$ n ∈ N , where U is uniformly distributed on [0, 1], $$(a_k)_{k\in {\mathbb {N}}}$$ ( a k ) k ∈ N is an Hadamard gap sequence, and $$f:{\mathbb {R}}\rightarrow {\mathbb {R}}$$ f : R → R is a 1-periodic, (Lipschitz-)continuous mapping. In the case of large gaps, we show that the normalized partial sums satisfy a large deviation principle at speed n and with a good rate function which is the sam

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22

Niemiec, Piotr. "Functor of extension in Hilbert cube and Hilbert space." Open Mathematics 12, no. 6 (2014). http://dx.doi.org/10.2478/s11533-013-0386-6.

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AbstractIt is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity, Lipschitz property, nonexpansiveness of maps in appropriate metrics.

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23

Fletcher, Alastair N., and Daniel A. Nicks. "Normal Families and Quasiregular Mappings." Proceedings of the Edinburgh Mathematical Society, October 23, 2023, 1–34. http://dx.doi.org/10.1017/s0013091523000640.

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Abstract Beardon and Minda gave a characterization of normal families of holomorphic and meromorphic functions in terms of a locally uniform Lipschitz condition. Here, we generalize this viewpoint to families of mappings in higher dimensions that are locally uniformly continuous with respect to a given modulus of continuity. Our main application is to the normality of families of quasiregular mappings through a locally uniform Hölder condition. This provides a unified framework in which to consider families of quasiregular mappings, both recovering known results of Miniowitz, Vuorinen and othe

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24

García, Rafael Espínola, and Aleksandra Huczek. "Structure of the set of fixed points of uniformly Lipschitzian semigroups in CAT(0) spaces." Topological Methods in Nonlinear Analysis, June 14, 2025, 1–14. https://doi.org/10.12775/tmna.2024.050.

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Fixed points for semigroups of $k$-Lipschitz mappings have been recently studied under the considerations that the semigroup satisfies a mild amenability condition or that it is left reversible. Both approaches have brought positive results on existence of fixed points and structure of the set of fixed points. In the case of the amenable condition, results have been obtained for Hilbert spaces; in the case of left reversible semigroups, results were first obtained for Hilbert spaces and then extended to $p$-uniformly convex spaces. In this work, we address both approaches in the non linear con

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25

Singh Saluja, Gurucharan. "CONVERGENCE THEOREMS OF A FAMILY OF UNIFORMLY (L, α)-LIPSCHITZ ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS". Demonstratio Mathematica 43, № 4 (2010). http://dx.doi.org/10.1515/dema-2010-0414.

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26

Saluja, Gurucharan Singh. "Convergence theorems of a family of uniformly (L, α)-Lipschitz asymptotically quasi-nonexpansive type mappings". Demonstratio Mathematica 43, № 4 (2010). http://dx.doi.org/10.1515/dema-2013-0271.

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