scholarly journals Rendezvous numbers in normed spaces

2005 ◽  
Vol 72 (3) ◽  
pp. 423-440 ◽  
Author(s):  
Bálint Farkas ◽  
Szilárd György Révész
Keyword(s):  
Banach Spaces ◽  
Metric Spaces ◽  
Lower Semicontinuous ◽  
Normed Spaces ◽  
Satisfactory Description ◽  
Infinite Dimensional ◽  
Compact Metric Spaces ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Chebyshev Constants

In previous papers, we used abstract potential theory, as developed by Fuglede and Ohtsuka, to a systematic treatment of rendezvous numbers. We considered Chebyshev constants and energies as two variable set functions, and introduced a modified notion of rendezvous intervals which proved to be rather nicely behaved even for only lower semicontinuous kernels or for not necessarily compact metric spaces.Here we study the rendezvous and average numbers of possibly infinite dimensional normed spaces. It turns out that very general existence and uniqueness results hold for the modified rendezvous numbers in all Banach spaces. We also observe the connections of these magical numbers to Chebyshev constants, Chebyshev radius and entropy. Applying the developed notions with the available methods we calculate the rendezvous numbers or rendezvous intervals of certain concrete Banach spaces. In particular, a satisfactory description of the case of Lp spaces is obtained for all p > 0.

Invariant measure for the Vasicek interest rate model in the Heath–Jarrow–Morton–Musiela framework

2015 ◽  
Vol 18 (03) ◽  
pp. 1550022 ◽  
Author(s):  
Francesco Cordoni ◽  
Luca Di Persio
Keyword(s):  
Invariant Measure ◽  
Stochastic Partial Differential Equation ◽  
Forward Rate ◽  
Infinite Dimensional ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Unique Invariant Measure

In this paper we study a particular class of forward rate problems, related to the Vasicek model, where the driving equation is a linear Gaussian stochastic partial differential equation. We first give an existence and uniqueness results of the related mild solution in infinite dimensional setting, then we study the related Ornstein–Uhlenbeck semigroup with respect to the determination of a unique invariant measure for the associated Heath–Jarrow–Morton–Musiela model.

scholarly journals On the Metric Compactification of Infinite-dimensional Spaces

2018 ◽  
Vol 62 (3) ◽  
pp. 491-507 ◽  
Author(s):  
Armando W. Gutiérrez
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Metric Spaces ◽  
Infinite Dimensional ◽  
Full Characterization ◽  
Geodesic Metric

AbstractThe notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel. It has been mainly studied on proper geodesic metric spaces. We present here a generalization of the metric compactification that can be applied to infinite-dimensional Banach spaces. Thereafter we give a complete description of the metric compactification of infinite-dimensional $\ell _{p}$ spaces for all $1\leqslant p<\infty$. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces.

scholarly journals Weighted fractional differential equations with infinite delay in Banach spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 370-383 ◽  
Author(s):  
Qixiang Dong ◽  
Can Liu ◽  
Zhenbin Fan
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Infinite Delay ◽  
Type Inequality ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractThis paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality is proved, and the comparison property of fractional integral is discussed.

scholarly journals ON FRACTIONAL VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH FRACTIONAL INTEGRABLE IMPULSES

2019 ◽  
Vol 24 (3) ◽  
pp. 457-477 ◽  
Author(s):  
Sagar T. Sutar ◽  
Kishor D. Kucche Kucche
Keyword(s):  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Integrodifferential Equations ◽  
Compact Interval ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Volterra Integrodifferential Equation

We consider a class of nonlinear fractional Volterra integrodifferential equation with fractional integrable impulses and investigate the existence and uniqueness results in the Bielecki’s normed Banach spaces. Further, Bielecki-Ulam type stabilities have been demonstrated on a compact interval. A concrete example is provided to illustrate the outcomes we acquired.

scholarly journals Geometry of the Banach spaces C(βN ×K,X) for compact metric spaces K

2011 ◽  
Vol 207 (2) ◽  
pp. 153-180 ◽  
Author(s):  
Dale E. Alspach ◽  
Elói Medina Galego
Keyword(s):  
Banach Spaces ◽  
Metric Spaces ◽  
Compact Metric Spaces

scholarly journals Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b -Metric Spaces over Banach Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yan Han ◽  
Shaoyuan Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
New Concepts ◽  
Lipschitz Constants ◽  
Asymptotically Regular ◽  
Type Contraction

In this paper, we firstly introduce the generalized Reich‐Ćirić‐Rus-type and Kannan-type contractions in cone b -metric spaces over Banach algebras and then obtain some fixed point theorems satisfying these generalized contractive conditions, without appealing to the compactness of X . Secondly, we prove the existence and uniqueness results for fixed points of asymptotically regular mappings with generalized Lipschitz constants. The continuity of the mappings is deleted or relaxed. At last, we prove that the completeness of cone b -metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X . Our results greatly extend several important results in the literature. Moreover, we present some nontrivial examples to support the new concepts and our fixed point theorems.

scholarly journals Common Best Proximity Point Theorems in JS-Metric Spaces Endowed with Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chaiporn Thangthong ◽  
Phakdi Charoensawan ◽  
Supreedee Dangskul ◽  
Narawadee Phudolsitthiphat
Keyword(s):  
Binary Relation ◽  
Directed Graph ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Edge Preserving ◽  
Common Best Proximity Point ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we introduce a notion of G -proximal edge preserving and dominating G -proximal Geraghty for a pair of mappings, which will be used to present some existence and uniqueness results for common best proximity points. Here, the mappings are defined on subsets of a JS-metric space endowed with a directed graph. An example is also provided to support the results. Moreover, we apply our result to a similar setting, where the JS-metric space is endowed with a binary relation.

scholarly journals Common fixed point theorems for asymptotically regular mappings on ordered orbitally complete metric spaces with an application to systems of integral equations

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3277-3289
Author(s):  
Hemant Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Integral Equations ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Systems Of Integral Equations ◽  
Weakly Increasing Maps ◽  
Asymptotically Regular

In this paper, we prove existence and uniqueness results for common fixed points of two or three relatively asymptotically regular mappings satisfying the orbital continuity of one of the involved maps on ordered orbitally complete metric spaces under generalized ?-contractive condition. Also, we introduce and use orbitally dominating maps and orbitally weakly increasing maps. We furnish suitable examples to demonstrate the usability of the hypotheses of our results. As an application, we prove the existence of solutions for certain system of integral equations.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

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