Limit of a sequence ≈ Limit of a sequence
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FROM THE SCHRODINGER PROBLEM TO THE MONGE-KANTOROVICH PROBLEM Open
The aim of this article is to show that the Monge-Kantorovich problem is the limit of a sequence of entropy minimization problems when a fluctuation parameter tends down to zero. We prove the convergence of the entropic values to the optim…
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The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces Open
The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces is established. The strong convergence of this technique is proved under certain assumptions imposed on the sequence of parameters. Moreover,…
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Finite mean field games: fictitious play and convergence to a first\n order continuous mean field game Open
In this article we consider finite Mean Field Games (MFGs), i.e. with finite\ntime and finite states. We adopt the framework introduced in Gomes Mohr and\nSouza in 2010, and study two seemly unexplored subjects. In the first one, we\nanaly…
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Scalar Curvature and Intrinsic Flat Convergence Open
Herein we present open problems and survey examples and theorems concerning sequences of Riemannian manifolds with uniform lower bounds on scalar curvature and their limit spaces. Examples of Gromov and of Ilmanen which naturally ought to …
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Discrete mean field games: Existence of equilibria and convergence Open
We consider mean field games with discrete state spaces (called discrete mean\nfield games in the following) and we analyze these games in continuous and\ndiscrete time, over finite as well as infinite time horizons. We prove the\nexistenc…
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The structure of spaces with Bakry–Émery Ricci curvature bounded below Open
We explore the structure of limit spaces of sequences of Riemannian manifolds with Bakry–Émery Ricci curvature bounded below in the Gromov–Hausdorff topology. By extending the techniques established by Cheeger and Cloding for Riemannian ma…
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On Rough ℐ<sub>2</sub>-Convergence of Double Sequences Open
In this study, we introduce the notion of rough ℐ_2-convergence and the set of rough ℐ_2-limit points of a double sequence and obtained two rough ℐ_2-convergence criteria associated with this set. Later, we proved that this set is closed a…
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On rough convergence in 2-normed spaces and some properties Open
In this study, we investigated relationships between rough convergence and classical convergence and studied some properties about the notion of rough convergence, the set of rough limit points and rough cluster points of a sequence in 2-n…
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Almost convergence of complex uncertain double sequences Open
Convergence of real sequences, as well as complex sequences are studied by B. Liu and X. Chen respectively in uncertain environment. In this treatise, we extend the study of almost convergence by introducing double sequences of complex unc…
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The emergence of torsion in the continuum limit of distributed edge-dislocations Open
We present a rigorous homogenization theorem for distributed dislocations. We\nconstruct a sequence of locally-flat Riemannian manifolds with dislocation-type\nsingularities. We show that this sequence converges, as the dislocations become…
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Approximation theorems for controllability problem governed by fractional differential equation Open
In this manuscript, we discuss the optimal control problem for a nonlinear system governed by the fractional differential equation in a separable Hilbert space . We utilize the fixed point technique and -resolvent family to present the exi…
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On statistically convergent sequences of closed sets Open
In this paper, we give the definitions of statistical inner and outer limits for sequences of closed sets in metric spaces. We investigate some properties of statistical inner and outer limits. For sequences of closed sets if its statistic…
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Weakly interacting oscillators on dense random graphs Open
We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e. two particles are interacting if and only if they are connected in the underlying g…
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Rigorous continuum limit for the discrete network formation problem Open
Motivated by recent papers describing the formation of biological transport networks we study a discrete model proposed by Hu and Cai consisting of an energy consumption function constrained by a linear system on a graph. For the spatially…
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Hölder continuity of tangent cones in RCD(K,N) spaces and applications to non-branching Open
In this paper we prove that a metric measure space $(X,d,m)$ satisfying the finite Riemannian curvature-dimension condition ${\sf RCD}(K,N)$ is non-branching and that tangent cones from the same sequence of rescalings are Hölder continuous…
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An Infinite System of Fractional Order with p-Laplacian Operator in a Tempered Sequence Space via Measure of Noncompactness Technique Open
In the current study, a new class of an infinite system of two distinct fractional orders with p-Laplacian operator is presented. Our mathematical model is introduced with the Caputo–Katugampola fractional derivative which is considered a …
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Convergence of Fibonacci–Ishikawa iteration procedure for monotone asymptotically nonexpansive mappings Open
In uniformly convex Banach spaces, we study within this research Fibonacci–Ishikawa iteration for monotone asymptotically nonexpansive mappings. In addition to demonstrating strong convergence, we establish weak convergence result of the F…
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On statistically convergent complex uncertain sequences Open
In this paper, we extend the study of statistical convergence of complex uncertain sequences in a given uncertainty space. We produce the relation between convergence and statistical convergence in an uncertain environment. We also initiat…
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On Zweier I-convergent double sequence spaces Open
In this article we introduce the Zweier I-convergent double sequence spaces 2ZI, 2ZI0 and 2ZI1. We prove the decomposition theorem and study topological properties, algebraic properties and some inclusion relations on these spaces.
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Statistical Convergence of Double Sequences in Neutrosophic Normed Spaces Open
In this paper, we define and study the notion of statistically convergent and statistically Cauchy double sequences in neutrosophic normed spaces. Moreover, we give the double statistically Cauchy sequence in neutrosophic normed space and …
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Convergence of nonlinear semigroups under nonpositive curvature Open
The present paper is devoted to gradient flow semigroups of convex functionals on Hadamard spaces. We show that the Mosco convergence of a sequence of convex lsc functions implies the convergence of the corresponding resolvents and the con…
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Bernstein fractal approximation and fractal full Müntz theorems Open
Fractal interpolation functions defined by means of suitable Iterated Function Systemsprovide a new framework for the approximation of continuous functions defined on a compact real interval.Convergence is one of the desirable properties o…
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Intrinsic flat Arzela–Ascoli theorems Open
One of the most powerful theorems in metric geometry is the Arzela-Ascoli Theorem which provides a continuous limit for sequences of equicontinuous functions between two compact spaces. This theorem has been extended by Gromov and Grove-Pe…
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The isoperimetric problem<i>via</i>direct method in noncompact metric measure spaces with lower Ricci bounds Open
We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact RCD( K, N ) spaces ( X , d, ℋ N ). Under the sole (necessary) assumption that the measure of unit balls is uniformly bounded away from ze…
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Convergence of Rothe scheme for a class of dynamic variational inequalities involving Clarke subdifferential Open
In the first part of the paper we deal with a second-order evolution variational inequality involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a time-semidiscr…
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Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings Open
In this study, at first we prove that the existence of best proximity points for cyclic nonexpansive mappings is equivalent to the existence of best proximity pairs for noncyclic nonexpansive mappings in the setting of strictly convex Bana…
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A Sequence of Kantorovich-Type Operators on Mobile Intervals Open
In this paper, we introduce and study a new sequence of positive linear operators, acting on both spaces of continuous functions as well as spaces of integrable functions on $[0, 1]$. We state some qualitative properties of this sequence a…
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dp–convergence and 𝜖–regularity theorems forentropy and scalar curvature lower bounds Open
Consider a sequence of Riemannian manifolds .M n i ; g i / whose scalar curvatures and entropies are bounded from below by small constants R i ; i i .The goal of this paper is to understand notions of convergence and the structure of limit…
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Rough I 2 ${I}_{2}$ -lacunary statistical convergence of double sequences Open
In this paper, we introduce and study the notion of rough -lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough -lacunary statistical limit set of a double sequence and d…
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Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces Open
This paper proposes rough convergence and rough statistical convergence of a double sequence in intuitionistic fuzzy normed spaces. It then defines the rough statistical limit points and rough statistical cluster points of a double sequenc…