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In this paper, we construct and investigate the space of null variable exponent second-order quantum backward difference sequences of fuzzy functions, which are crucial additions to the concept of modular spaces. The idealization of the mappings has been achieved through the use of extended s − fuzzy functions and this sequence space of fuzzy functions. This new space's topological and geometric properties and the mappings' ideal that corresponds to them are discussed. We construct the existence of a fixed point of Kannan contraction mapping acting on this space and its associated pre-quasi ideal. To demonstrate our findings, we give a number of numerical experiments. There are also some significant applications of the existence of solutions to nonlinear difference equations of fuzzy functions. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme for solving a class of boundary value problems of second-order ordinary differential equations (ODEs) and analyze the error and the convergence of this method. The results show that the algorithm is high accurate and conditionally convergent, and an accuracy of 1 / 240 h 6 was achieved with smooth functions. [ABSTRACT FROM AUTHOR]

We establish a new blow-up criteria for solution of the three-dimensional Boussinesq equations in Triebel-Lizorkin spaces by using Littlewood-Paley decomposition. [ABSTRACT FROM AUTHOR]

We introduce a new space ANlog,α(픹) consisting of all holomorphic functions on the unit ball 픹 ⊂ ℂn such that ||f||ANlog,α ≔ ∫픹φe(ln(1 + |f(z)|))dVα(z) < ∞, where α > -1, dVα(z) = cα,n(1 - |z|²)α dV (z) (dV (z) is the normalized Lebesgue volume measure on 픹, and cα,n is a normalization constant, that is, Vα(픹) = 1), and φe(t) = t ln(e + t) for t ∈ [0,∞). Some basic properties of this space are presented. Among other results we proved that ANlog,α(픹) with the metric d(f, g) = ||f - g||ANlog,α is an F-algebra with respect to pointwise addition and multiplication. We also prove that every linear isometry T of ANlog,α(픹) into itself has the form Tf = c(f ο ψ) for some c ∈ ℂ such that |c| = 1 and some ψ which is a holomorphic self-map of 픹 satisfying a measure-preserving property with respect to the measure dVα. As a consequence of this result we obtain a complete characterization of all linear bijective isometries of ANlog,α(픹). [ABSTRACT FROM AUTHOR]

We determine the weakly asymptotically orders for the average errors of the Grünwald interpolation sequences based on the Tchebycheff nodes in the Wiener space. By these results we know that for the Lp-norm (2 ≤ q ≤ 4) approximation, the p-average (1 ≤ p ≤ 4) error of some Grünwald interpolation sequences is weakly equivalent to the p-average errors of the best polynomial approximation sequence. [ABSTRACT FROM AUTHOR]

We give new and very general characterizations for uniform exponential dichotomy of variational difference equations in terms of the admissibility of pairs of sequence spaces over ℕ with respect to an associated control system. We establish in the variational case the connections between the admissibility of certain pairs of sequence spaces over N and the admissibility of the corresponding pairs of sequence spaces over ℤ. We apply our results to the study of the existence of exponential dichotomy of linear skew-product flows. [ABSTRACT FROM AUTHOR]

The article presents information on a study which investigated nonlocal boundary value problems for elliptic-parabolic differential and difference equations. The study assesses the well-posedness of this problem in Hölder spaces with a weight and the coercivity inequalities for the solution of boundary value problems for elliptic-parabolic equations. The study also offers information on the first order of accuracy difference scheme for the approximate solution of this nonlocal boundary value problem.