775 Results Found

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...

The concept of the deferred Nörlund equi-statistical convergence was introduced and studied by Srivastava et al. [Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. (RACSAM) 112 (2018), 1487–1501]. In the present paper, we have st...

We start by an application the of Krein–Milman theorem to the integral representation of completely monotonic functions. Elements of convex optimization are also mentioned. The paper continues with applications of Hahn–Banach-type theorem...

We review earlier and recent results on the Markov moment problem and related polynomial approximation on unbounded subsets. Such results allow proving the existence and uniqueness of the solutions for some Markov moment problems. This is the first a...

In this paper, we define and study q-statistical limit point, q-statistical cluster point, q-statistically Cauchy, q-strongly Cesàro and statistically $C_1^q$-summable sequences. We establish relationships of q-statistical convergence with q-statisticall...

The concept of statistically deferred-weighted summability was recently studied by Srivastava et al. (Math. Methods Appl. Sci. 41 (2018), 671–683). The present work is concerned with the deferred-weighted summability mean in various aspects def...

In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fun...

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 functi...

Here, in this article, we introduce and systematically investigate the ideas of deferred weighted statistical Riemann integrability and statistical deferred weighted Riemann summability for sequences of functions. We begin by proving an inclusion the...

This paper investigates fundamental concepts of statistical convergence for double sequences of time-scale functions via the deferred Cesàro summability mean. Several limit properties and inclusion relations between the newly-introduced conver...

The present review paper provides recent results on convexity and its applications to the constrained extension of linear operators, motivated by the existence of subgradients of continuous convex operators, the Markov moment problem and related Mark...

We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation...

In this paper, we introduce and investigate a new class of the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of the classical Baskakov-Schurer-Szász-Stancu approximation oper...

In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we state an a...

In this paper, we introduce and investigate a hybrid type of nonlinear Riemann Liouville fractional integro-differential equations. We develop and extend previous work on such non-fractional equations, using operator theoretical techniques, and find...

This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence a...

In this study, a new kind of modified $\lambda$-Bernstein-Stancu operators is constructed. Compared with the original $\lambda$-Bézier basis function, the newly operator basis function is more concise in form and has certain symmetry beauty. The...

The Kolmogorov–Arnold representation theorem states that any continuous multivariable function can be exactly represented as a finite superposition of continuous single-variable functions. Subsequent simplifications of this representation invol...

In the realm of generalized modular metric spaces, we substantiate the validity of fixed-point theorems with Branciari contractions. This paper expands and broadens the original theorems in this context. Subsequently, by building upon this foundation...

We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter $\lambda \in [-1,1]$ and calculate their moments. The uniform convergence of the operator and global approximation result by means of...

In spectral/finite element methods, a robust and stable high-order polynomial approximation method for the solution can significantly reduce the required number of degrees of freedom (DOFs) to achieve a certain level of accuracy. In this work, a clos...

Approximation and some other basic properties of various linear and nonlinear operators are potentially useful in many different areas of researches in the mathematical, physical, and engineering sciences. Motivated essentially by this aspect of appr...

Determining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuab...

This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various funct...

This research work focuses on $\lambda$-Szász–Mirakjan operators coupling generalized beta function. The kernel functions used in $\lambda$-Szász operators often possess even or odd symmetry. This symmetry influences the behavior of the operator in terms of approxim...

In this work, we first establish a new connection between adjoint Bernoulli’s polynomials and gamma function as a new sequence of linear positive operators denoted by ${\mathfrak{S}}_{r,\varsigma ,\lambda }(.;.)$. Further, convergence results for these sequences o...

This paper is devoted to studying the statistical approximation properties of a sequence of univariate and bivariate blending-type Bernstein operators that includes shape parameters $\alpha$ and $\lambda$ and a positive integer. An estimate of the corr...

The goal of this manuscript is to introduce a new Stancu generalization of the modified Szász–Kantorovich operator connecting Riemann–Liouville fractional operators via Charlier polynomials. Further, some estimates are calculated as test functions an...

This paper aims to extend, within the context of quantum calculus, the $\alpha$-Bernstein–Schurer operators ($\alpha \in [0,1]$) to Kantorovich form. Using the Ditzian–Totik modulus of continuity and the Lipschitz-kind maximal function for...

In this paper, we consider functional set-valued differential equations in their integral representations that possess integrals symmetrically on both sides of the equations. The solutions have values that are the nonempty compact and convex subsets....

This paper introduces a novel family of positive linear operators constructed by blending degenerate Appell polynomials with a classical Beta kernel in the Durrmeyer setting. The operators are defined as $H_n(g;u)=\sum _{ƿ=0}^{\infty }{h}_{ƿ}(n+u;ƛ$...

In this paper, we defined weighted $(E_{\lambda },q)(C_{\lambda },1)$ statistical convergence. We also proved some properties of this type of statistical convergence by applying $(E_{\lambda },q)(C_{\lambda },1)$ summability method. Moreover, we used $(E_{\lambda },q)(C_{}$...

The paper is devoted to Epstein zeta-function ${\zeta }_3\left(s\right)$, $s=\sigma +it$, of a quadratic form of three variables. We obtain a probabilistic characterization of the function ${\zeta }_3\left(s\right)$ in terms of weak convergence of probability measures in the space of...

This study focuses on approximating continuous functions using Frobenius–Euler–Simsek polynomial analogues of Szász operators. Test functions and central moments are computed to study convergence uniformly, approximation order by t...

In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous fun...

The Taylor approximation theorem is a fundamental tool in numerical analysis, providing a local polynomial representation of smooth functions. In practical computations, a function f is approximated by a finite Taylor polynomial $P_n$, and controlling t...

In this paper, the finite-approximate controllability for a class of fractional composite relaxation equations with different nonlocal conditions is discussed. Firstly, under the condition that the nonlocal term is compact, the existence of mild solu...

The primary objective of this study is to investigate the concept of approximate controllability in fractional evolution equations that involve the ψ-Caputo derivative. Specifically, we examine the scenario where the semigroup is compact and anal...

The full discrete approximation of solutions of nonhomogeneous fractional equations is considered in this paper. The methods of iteration, finite differences and projection are applied to obtain desired formulas of explicit- and implicit-difference s...

In this manuscript, we investigate the issue of approximate controllability for a certain class of abstract neutral integro-differential equations having non-instantaneous impulsions and being subject to state-dependent delay. Our methodology relies...

The objective of this paper is to analyze the approximate controllability of a semilinear stochastic integrodifferential system with nonlocal conditions in Hilbert spaces. The nonlocal initial condition is a generalization of the classical initial co...

We calculate the metric of a self-gravitating and collapsing infinitely thin spherical shell in the weak-field and slow-motion limits, and we demonstrate that Birkhoff’s theorem is not consistent with the theory of the post-Newtonian approximat...

The existence, uniqueness, and Carath$\acute{\mathrm{e}}$odory’s successive approximation of the fractional neutral stochastic differential equation (FNSDE) in Hilbert space are considered in this paper. First, we give the Carath$\acute{\mathrm{e}}$odory’s appro...

We study practical approximations of Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the optimality of the interpreter for this language as the reference machine for the Coding Theorem Met...

Let $\mathfrak{a}=\{a_m:m\in \mathbb{N}\}$ be a multiplicative periodic sequence of complex numbers. In this paper, we consider the approximation of analytic functions defined in the strip $\{s=\sigma +it:1/2<\sigma <1\}$ by shifts $\zeta (s+i\tau ;\mathfrak{a})$ of the zeta-function...

The paper deals with the results of a study of a third-order nonlinear differential equation with moving singular points and critical poles. So far, this type of equation cannot be solved in quadratures. The development of the author’s approach...

This article primarily focuses on the approximate controllability of fractional semilinear integrodifferential equations using resolvent operators. Two alternative sets of necessary requirements have been studied. In the first set, we use theories fr...

This article introduces new sufficient conditions ensuring the interior approximate controllability of semilinear thermoelastic plate equations subject to Dirichlet boundary conditions. The analysis is carried out by reformulating the system as an ab...

In the paper, we consider the approximation of analytic functions by shifts from the wide class $\tilde{S}$ of L-functions. This class was introduced by A. Selberg, supplemented by J. Steuding, and is defined axiomatically. We prove the so-called joint...

This paper investigates a class of nonlinear fractional differential equations with boundary value problems involving Caputo–Hadamard-type derivatives. By relaxing the monotonicity constraints on the nonlinear terms and considering more general...