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Items from 1 to 20 out of 1,250 results

article

On the convergence of inexact two-point Newton-like methods on Banach spaces

Ioannis Konstantinos Argyros, Ángel Alberto Magreñán, I.K. Argyros, A.A. Magrenan

Applied Mathematics and Computation > 2015 > 265 > Complete > 893-902

We present a unified convergence analysis of Inexact Newton-like methods in order to approximate a locally unique solution of a nonlinear operator equation containing a nondifferentiable term in a Banach space setting. The convergence conditions are more general and the error analysis more precise than in earlier studies such as (Argyros, 2007; Cătinaş, 2005; Cătinaş, 1994; Chen and Yamamoto, 1989;...

article

Constrained Conditional Moment Restriction Models

Victor Chernozhukov, Whitney K. Newey, Andres Santos

Econometrica > 91 > 2 > 709 - 736

Shape restrictions have played a central role in economics as both testable implications of theory and sufficient conditions for obtaining informative counterfactual predictions. In this paper, we provide a general procedure for inference under shape restrictions in identified and partially identified models defined by conditional moment restrictions. Our test statistics and proposed inference methods...

article

A global solvability of a two‐dimensional kernel determination problem for a viscoelasticity equation

Zhanna D. Totieva

Mathematical Methods in the Applied Sciences > 45 > 12 > 7555 - 7575

Under study is the two‐dimensional inverse problem of determining the convolutional kernel of the integral term in a viscoelasticity equation. The direct problem is represented by a generalized initial‐boundary value problem for this equation with zero initial data and the Neumann boundary condition in the form of the Dirac delta function. For solving the inverse problem, the traces of the solution...

article

Extended convergence for a fifth‐order novel scheme free from derivatives

Ramandeep Behl, Ioannis K. Argyros, Eulalia Martínez, Janak Joshi

Mathematical Methods in the Applied Sciences > 45 > 6 > 3295 - 3304

The objective in this paper is the expansion of the utilization for a fifth convergence order scheme without derivatives for finding solutions of Banach space valued equations. Conditions of the first order divided difference of the operator involved are only imposed. In this way the use of the scheme is expanded, since in earlier articles the derivatives until order four that do appear in the iterative...

article

An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

Oluwatosin T. Mewomo, Olawale K. Oyewole

Demonstratio Mathematica > 2021 > Vol. 54, nr 1 > 335--358

In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the...

article

The Henstock‐Kurzweil‐Pettis integral and multiorders fractional differential equations with impulses and multipoint fractional integral boundary conditions in Banach spaces

Djamila Seba, Sadek Habani, Abbes Benaissa, Hamza Rebai

Mathematical Methods in the Applied Sciences > 44 > 10 > 8345 - 8362

This paper is devoted to the existence of weak solutions for a multipoint fractional integral boundary value problem of an impulsive nonlinear differential equation involving multiorders fractional derivatives and deviating argument. We make use of an appropriate fixed point theorem combined with the technique of measures of weak noncompactness. Our investigation is considered in a Banach space. The...

article

Extended and unified local convergence of k‐step solvers for equations with applications

Ramandeep Behl, Ioannis K. Argyros, Ali Saleh Alshomrani

Mathematical Methods in the Applied Sciences > 44 > 9 > 7747 - 7755

There is a plethora of k‐step solvers for equations involving operators on Banach spaces. Their convergence is estimated by adopting hypotheses on high‐order derivatives which are not even in these iterative solvers. In addition, no computable error bounds or information on the uniqueness of the solution based on Lipschitz‐type functions are given. Moreover, the choice of the initial guess is like...

article

Hausdorff‐Young inequalities and multiplier theorems for quaternionic operator‐valued Fourier transforms

Pan Lian

Mathematical Methods in the Applied Sciences > 44 > 8 > 6601 - 6611

Due to the non‐commutativity of quaternions, there are three kinds of quaternionic Banach spaces, i.e. the right sided, the left sided, and the two sided ones. For the left and right sided Banach spaces, the quaternion multiplications are only defined on one single side. In this paper, we characterize the quaternionic Banach spaces such that the quaternionic operator valued Fourier transforms satisfy...

article

Modeling and simulation of fractional order COVID‐19 model with quarantined‐isolated people

Muhammad Aslam, Muhammad Farman, Ali Akgül, Meng Sun

Mathematical Methods in the Applied Sciences > 44 > 8 > 6389 - 6405

The dynamics of diseases and effectiveness of control policies play important role in the prevention of epidemic diseases. To this end, this paper is concerned with the design of fractional order coronavirus disease (COVID‐19) model with Caputo Fabrizio fractional derivative operator of order Ω ∈ (0, 1] for the COVID‐19. Verify the nonnegative special solution and convergence of the scheme with in...

article

Eigenmeasures and stochastic diagonalization of bilinear maps

Ezgi Erdoğan, Enrique A. Sánchez Pérez

Mathematical Methods in the Applied Sciences > 44 > 6 > 5021 - 5039

A new stochastic approach is presented to understand general spectral type problems for (not necessarily linear) functions between topological spaces. In order to show its potential applications, we construct the theory for the case of bilinear forms acting in couples of a Banach space and its dual. Our method consists of using integral representations of bilinear maps that satisfy particular domination...

article

Approximate multi-Jensen-cubic mappings and a fixed point theorem

Elahe Ramzanpour, Abasalt Bodaghi

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2020 > 19 > 141-154

In this paper, we introduce multi-Jensen-cubic mappings and unify the system of functional equations defining the multi-Jensen-cubic mapping to a single equation. Applying a fixed point theorem, we establish the generalized Hyers-Ulam stability of multi-Jensen-cubic mappings. As a known outcome, we show that every approximate multi-Jensen-cubic mapping can be multi-Jensen-cubic.

article

The norming set of a bilinear form on l2∞

Sung Guen Kim

Commentationes Mathematicae > 2020 > Vol. 60, No. 1/2 > 37--63

An element (x₁,…, x_n) ∈ Eⁿ is called a norming point of T ∈ L(ⁿE) if ∥x₁∥ = ⋯ = ∥x_n∥ = 1 and ∣T(x₁,…, x_n)∣ = ∥T∥, where L(ⁿE) denotes the space of all continuous n-linear forms on E. For T ∈ L(ⁿE), we define Norm (T) = {(x₁,…, x_n) ∈ Eⁿ: (x₁,…, x_n) is a norming point of T}. Norm (T) is called the norming set of T. We classify Norm (T) for every T ∈ L(²l²_∞).

article

A fixed point application for the stability and hyperstability of multi-Jensen-quadratic mappings

Somaye Salimi, Abasalt Bodaghi

Journal of Fixed Point Theory and Applications > 2020 > 22 > 1 > 1-15

In this paper, we unify the system of functional equations defining a multi-Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers–Ulam stability of such equation and thus generalizing some known results. As a result, we show that the multi-Jensen-quadratic functional equation is hyperstable.

article

Normal structure and fixed point properties for some Banach algebras

Abdelkader Dehici

Journal of Fixed Point Theory and Applications > 2020 > 22 > 1 > 1-18

In this paper, we investigate key assumptions on some Banach algebras to have quasi-weak normal structure (resp. $$\hbox {quasi-weak}^{\star }$$ quasi-weak⋆ normal structure) and to prove in particular that fixed point property for Kannan mappings is satisfied on weakly compact convex subsets in this setting. We establish some conditions on a locally compact group G for which the Fourier and Fourier–Stieltjes–Banach...

article

Generalized Transportation Cost Spaces

Sofiya Ostrovska, Mikhail I. Ostrovskii

Mediterranean Journal of Mathematics > 2019 > 16 > 6 > 1-26

The paper is devoted to the geometry of transportation cost spaces and their generalizations introduced by Melleray et al. (Fundam Math 199(2):177–194, 2008). Transportation cost spaces are also known as Arens–Eells, Lipschitz-free, or Wasserstein 1 spaces. In this work, the existence of metric spaces with the following properties is proved: (1) uniformly discrete metric spaces such that transportation...

article

Embedding Banach spaces into the space of bounded functions with countable support

William B. Johnson, Tomasz Kania

Mathematische Nachrichten > 292 > 9 > 2028 - 2031

We prove that a WLD subspace of the space

ℓ_{\infty}^{c} (Γ)

consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into

ℓ_{\infty}

if and only if it does not contain isometric copies of

c_{0} (ω_{1})

. Moreover, a subspace of

ℓ_{\infty}^{c} (ω_{1})

is constructed that has an unconditional basis, does not embed into

ℓ_{\infty}

, and whose every weakly compact subset is separable (in particular, it cannot contain any...

article

Some Spaces of Harmonic Functions in the Unit Ball of ℝⁿ

A. I. Petrosyan

Lobachevskii Journal of Mathematics > 2019 > 40 > 8 > 1132-1136

We introduce the Banach spaces h_∞(ϕ), h₀(ϕ) and h¹(ψ) functions harmonic in the unit ball B ⊂ ℝⁿ. These spaces depend on weight functions ϕ, ψ. We prove that if ϕ and ψ form a normal pair, then h¹(ψ)* ∼ h_∞(ϕ) and h₀(ϕ)* ∼ h¹(ψ).

article

The Steiner Subratio in Banach Spaces

L. Sh. Burusheva

Mathematical Notes > 2019 > 106 > 1-2 > 183-190

For every n = 2, 3,…, the minimum of the Steiner subratio is found for n-point sets in Banach spaces, and an example of a Banach space is constructed for which this minimum is attained. An example of a Banach space for which the minimum possible Steiner subratio equals 1/2 is also constructed.

article

Multiquartic functional equations

Abasalt Bodaghi, Choonkil Park, Oluwatosin T. Mewomo

Advances in Difference Equations > 2019 > 2019 > 1 > 1-10

In this paper, we study n-variable mappings that are quartic in each variable. We show that the conditions defining such mappings can be unified in a single functional equation. Furthermore, we apply an alternative fixed point method to prove the Hyers–Ulam stability for the multiquartic functional equations in the normed spaces. We also prove that under some mild conditions, every approximately multiquartic...

article

On a Problem for a Quasi-Linear Equation of Even Order

A. V. Yuldasheva

Journal of Mathematical Sciences > 2019 > 241 > 4 > 423-429

We study a boundary-value problem for a quasi-linear equation of even order with periodic boundary conditions. We prove the existence and uniqueness of a weak generalized solution.

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Search results

On the convergence of inexact two-point Newton-like methods on Banach spaces

Constrained Conditional Moment Restriction Models

A global solvability of a two‐dimensional kernel determination problem for a viscoelasticity equation

Extended convergence for a fifth‐order novel scheme free from derivatives

An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

The Henstock‐Kurzweil‐Pettis integral and multiorders fractional differential equations with impulses and multipoint fractional integral boundary conditions in Banach spaces

Extended and unified local convergence of k‐step solvers for equations with applications

Hausdorff‐Young inequalities and multiplier theorems for quaternionic operator‐valued Fourier transforms

Modeling and simulation of fractional order COVID‐19 model with quarantined‐isolated people

Eigenmeasures and stochastic diagonalization of bilinear maps

Approximate multi-Jensen-cubic mappings and a fixed point theorem

The norming set of a bilinear form on l2∞

A fixed point application for the stability and hyperstability of multi-Jensen-quadratic mappings

Normal structure and fixed point properties for some Banach algebras

Generalized Transportation Cost Spaces

Embedding Banach spaces into the space of bounded functions with countable support

Some Spaces of Harmonic Functions in the Unit Ball of ℝⁿ

The Steiner Subratio in Banach Spaces

Multiquartic functional equations

On a Problem for a Quasi-Linear Equation of Even Order

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