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In this paper, we prove a couple of approximation results for local existence and uniqueness of solution of an IVP of nonlinear first order ordinary hybrid differential equations under weaker compactness and Lipschitz conditions by using the Dhage monotone iteration method based on a recent hybrid fixed point theorem of Dhage (2022) and Dhage et al. (2022). An approximation result for the Ulam-Hyers stability of the local solution of the considered hybrid differential equation is also established. Our main abstract results are also illustrated with a couple of numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we establish two approximation theorems for the multidimensional fractional Fourier transform via appropriate convolutions. As applications, we study the boundary and initial problems of the Laplace and heat equations with chirp functions. Furthermore, we obtain the general Heisenberg inequality with respect to the multidimensional fractional Fourier transform. [ABSTRACT FROM AUTHOR]

Assume that and , with . Assume further that and are bounded domains in , with , such that and the complement has no nonempty compact components in . We study the approximation of solutions in the Lebesgue space to parabolic Lamé-type operators in the cylindrical domain by more regular solutions in the larger domain . As application of the approximation theorems, we construct some Carleman formulas for recovering solutions to these parabolic operators in the Sobolev space via the values of the solutions and the corresponding stress tensors on a part of the lateral surface of the cylinder. [ABSTRACT FROM AUTHOR]

In this paper, we defined weighted (E λ , q) (C λ , 1) statistical convergence. We also proved some properties of this type of statistical convergence by applying (E λ , q) (C λ , 1) summability method. Moreover, we used (E λ , q) (C λ , 1) summability theorem to prove Korovkin's type approximation theorem for functions on general and symmetric intervals. We also investigated some of the results of the rate of weighted (E λ , q) (C λ , 1) statistical convergence and studied some sequences spaces defined by Orlicz functions. [ABSTRACT FROM AUTHOR]

The means to obtain the adsorption isotherms is a fundamental open problem in competitive chromatography. A modern technique of estimating adsorption isotherms is to solve a nonlinear inverse problem in a partial differential equation so that the simulated batch separation coincides with actual experimental results. However, this identification process is usually ill-posed in the sense that the uniqueness of adsorption isotherms cannot be guaranteed, and moreover, the small noise in the measured response can lead to a large fluctuation in the traditional estimation of adsorption isotherms. The conventional mathematical method of solving this problem is the variational regularization, which is formulated as a non-convex minimization problem with a regularized objective functional. However, in this method, the choice of regularization parameter and the design of a convergent solution algorithm are quite difficult in practice. Moreover, due to the restricted number of injection profiles in experiments, the types of measured data are extremely limited, which may lead to a biased estimation. In order to overcome these difficulties, in this paper, we develop a new inversion method – the virtual injection promoting double feed-forward neural network (VIP-DFNN). In this approach, the training data contain various types of artificial injections and synthetic noisy measurement at outlet, generated by a conventional physics model – a time-dependent convection-diffusion system. Numerical experiments with both artificial and real data from laboratory experiments show that the proposed VIP-DFNN is an efficient and robust algorithm. [ABSTRACT FROM AUTHOR]

A criterion for the approximability of all solutions of the heat equation in a bounded cylindrical domain that belong to the Lebesgue class by more regular (e.g., Sobolev) solutions of the same equation in a bounded cylindrical domain with larger base is obtained. Namely, the complement of the smaller base to the larger one must have no (nonempty connected) compact components. As an important corollary, we prove a theorem on the existence of a doubly orthogonal basis for the corresponding pair of Hilbert spaces. [ABSTRACT FROM AUTHOR]

The present paper emphasises on equi-statistical convergence, pointwise statistical convergence and uniform statistical convergence for a sequence of real-valued functions by using deferred Cesàro and deferred Euler statistical convergence and obtain various implicative results with supporting examples. We make an effort to demonstrate Korovkin-type approximation theorem via deferred Cesàro and deferred Euler equi-statistical convergence. We also present an example which shows that our Korovkin-type theorem is powerful than its classical version. Further, we study rates of deferred Cesàro and deferred Euler equi-statistical convergence via modulus of continuity. [ABSTRACT FROM AUTHOR]

The paper aims to investigate different types of weighted statistical convergence and weighted statistical summability of double sequences of fuzzy numbers. Relations connecting statistical convergence and statistical summability have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. Relevant inclusion relations and related results concerning the new fuzzy summability methods have also been examined in detail. Finally, a Korovkin-type approximation theorem for double sequences of fuzzy positive linear operators has been established using the most generalized version of the summability method and showed its efficiency by means of a concrete example. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the new concept of weighted statistical convergence and strong weighted summability of order β for sequences of fuzzy numbers involving the ideas of difference operators and two sequences , of positive numbers, and establish the relationship between these notions. Finally, as an application, we apply our notion of weighted -statistical of order β with a view to proving fuzzy Korovkin-type approximation theorem and provide an interesting example to illustrate our approximation result. [ABSTRACT FROM AUTHOR]

Despite the fact that call-by-value λ-calculus was defined by Plotkin in 1977, we believe that its theory of program approximation is still at the beginning. A problem that is often encountered when studying its operational semantics is that, during the reduction of a λ-term, some redexes remain stuck (waiting for a value). Recently, Carraro and Guerrieri proposed to endow this calculus with permutation rules, naturally arising in the context of linear logic proof-nets, that succeed in unblocking a certain number of such redexes. In the present paper we introduce a new class of models of call-by-value λ-calculus, arising from non-idempotent intersection type systems. Beside satisfying the usual properties as soundness and adequacy, these models validate the permutation rules mentioned above as well as some reductions obtained by contracting suitable λI-redexes. Thanks to these (perhaps unexpected) features, we are able to demonstrate that every model living in this class satisfies an Approximation Theorem with respect to a refined notion of syntactic approximant. While this kind of results often require impredicative techniques like reducibility candidates, the quantitative information carried by type derivations in our system allows us to provide a combinatorial proof. [ABSTRACT FROM AUTHOR]

For the principle eigenvalue of discrete weighted p-Laplacian on the set of nonnegative integers, the convergence of an approximation procedure and the inverse iteration is proved. Meanwhile, in the proof of the convergence, the monotonicity of an approximation sequence is also checked. To illustrate these results, some examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we investigate sufficient and necessary conditions of uniform local exponential stability (ULES) for the discrete-time nonlinear switched system (DTNSS). We start with the definition of T-step common Lyapunov functions (CLFs), which is a relaxation of traditional CLFs. Then, for a time-varying DTNSS, by constructing such a T-step CLF, a necessary and sufficient condition for its ULES is provided. Afterwards, we strengthen it based on a T-step Lipschitz continuous CLF. Especially, when the system is time-invariant, by the smooth approximation theorem, the Lipschitz continuity condition of T-step CLFs can further be replaced by continuous differentiability; and when the system is time-invariant and homogeneous, due to the extension of Weierstrass approximation theorem, T-step continuously differentiable CLFs can even be strengthened to be T-step polynomial CLFs. Furthermore, three illustrative examples are additionally used to explain our main contribution. In the end, an equivalence between time-varying DTNSSs and their corresponding linearisations is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we consider an approximation sequence of a common fixed point generated by Halpern type iteration with a finite family of nonexpansive mappings in a Hadamard space. We propose another style of Halpern type iteration with multiple anchor points and prove that it converges strongly to a common fixed point. [ABSTRACT FROM AUTHOR]

In this work, we use the notion of (λ, μ)-statistical convergence to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1, x, y, x² + y². Furthermore, we define a new type of summability method via (λ, μ)-statistical convergence and use it to prove Korovkin theorem. Moreover, we obtain order of (λ, μ)-statistical convergence in our approximation. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to an approximation theorem of semigroups of Lipschitz operators which are closely related with the abstract Cauchy problem and an application of the obtained result to the projection method for the two-dimensional Navier–Stokes equations. [Copyright &y& Elsevier]

In this work, we use the notion of (λ, μ)-statistical convergence to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1, x, y, x² + y². Furthermore, we define a new type of summability method via (λ, μ)-statistical convergence and use it to prove Korovkin theorem. Moreover, we obtain order of (λ, μ)-statistical convergence in our approximation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the author defines Bernstein type rational functions of two variables and prove the approximation theorems for the derivatives of them. [Copyright &y& Elsevier]

We investigate a new representation of general operators by means of sums of shifted Gabor multipliers. These representations arise by studying the matrix of an operator with respect to a Gabor frame. Each shifted Gabor multiplier corresponds to a side-diagonal of this matrix. This representation is especially useful for operators whose associated matrix possesses some off-diagonal decay. In this case one can completely characterize the symbol class of the operator by the size of the symbols of the Gabor multipliers. As an application we derive approximation theorems for pseudodifferential operators in the Sjostrand class. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we define a new type of summability method via statistical convergence by using the density and -summability. We further apply our new summability method to prove a Korovkin type approximation theorem. [ABSTRACT FROM AUTHOR]

In the papers [5]-[7] was examined approximation of functions by the modified Szász-Mrakyan operators and other positive linear operators preserving e²(x) = x²: In this paper we introduce the Post-Widder and Stancu operators preserving x² in polynomial weighted spaces. We show that these operators have better approximation properties than classical Post-Widder and Stancu operators. [ABSTRACT FROM AUTHOR]

Efroymson's Approximation Theorem asserts that if f is a C 0 semialgebraic mapping on a C ∞ semialgebraic submanifold M of R n and if ε : M → R is a positive continuous semialgebraic function then there is a C ∞ semialgebraic function g : M → R such that | f − g | < ε. We prove a generalization of this result to the globally subanalytic category. Our theorem actually holds in a larger framework since it applies to every function which is definable in a polynomially bounded o-minimal structure (expanding the real field) that admits C ∞ cell decomposition. We also establish approximation theorems for Lipschitz and C 1 definable functions. [ABSTRACT FROM AUTHOR]

In this paper, our purpose is to investigate the vector equilibrium problem of whether the approximate solution representing bounded rationality can converge to the exact solution representing complete rationality. An approximation theorem is proved for vector equilibrium problems under some general assumptions. It is also shown that the bounded rationality is an approximate way to achieve the full rationality. As a special case, we obtain some corollaries for scalar equilibrium problems. Moreover, we obtain a generic convergence theorem of the solutions of strictly-quasi-monotone vector equilibrium problems according to Baire's theorems. As applications, we investigate vector variational inequality problems, vector optimization problems and Nash equilibrium problems of multi-objective games as special cases. [ABSTRACT FROM AUTHOR]

In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon’s bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the solutions of monotone equilibrium problems in the sense of Baire category. As applications, we investigate the optimization problem, variational inequality problem and saddle point problem as special cases. [ABSTRACT FROM AUTHOR]