Here are studied in terms of multivariate fuzzy high approximation to the multivariate unit basic sequences of multivariate fuzzy neural network operators. These operators are multivariate fuzzy analogs of earlier studied multivariate real ones. The produced results generalize earlier real ones into the fuzzy setting. Here the high order multi-variate fuzzy pointwise convergence with rates to the multivariate fuzzy unit operator is established through multivariate fuzzy inequalities involving the multivariate fuzzy moduli of continuity of the Nth order (N <img border=0 width=28 height=21 src="http:/fbpe/img/cubo/v16n3/art03-a.jpg">1) H-fuzzy partial derivatives, of the engaged multivariate fuzzy number valued function.

Utilizando aproximaciones multivariadas difusas superiores, estudiamos la aplicación a secuencias basicas unitarias multivariadas de operadores de redes neuronales disfusas multivariadas. Estos operadores son analogos difusos multivariados de los reales multi-variados estudiados anteriormente. Los resultados obtenidos generalizan los resultados reales anteriores en el marco difuso. La convergencia puntual difusa multivariada de orden superior con velocidades para los operadores unitarios difusos multivariados se establece a travóes de desigualdades difusas multivariadas que involucran los móodulos de continuidad difusos multivariados de las derivadas parciales H-difusas de N-ésimo orden ( N <img border=0 width=28 height=21 src="http:/fbpe/img/cubo/v16n3/art03-a.jpg">1 ) de las funciones con valores numóericos difusos multivariados

Let E be a vector valued sequence space with â-dual Åâã. We consider sufficient conditions on E for the series in a pointwise bounded subset of Åâã to be uniformly convergent over certain subsets of E. The conditions involve gliding hump assumptions on the multiplier space E. Applications to matrix mappings between vector valued sequence spaces are given.

In this article we study the approximation properties of general singular integral operators over the real line. We establish their convergence to the unit operator with rates. The estimates are mostly sharp and they are pointwise or uniform. The established inequalities involve the higher order modulus of smoothness. We apply this theory to the trigonometric singular operators.

En este artículo estudiamos propiedades de aproximación de operadores integrales singulares generales sobre la recta real. Establecemos su convergencia al operador unidad con las tasas correspondientes. Las estimaciones son mayormente ajustadas y son tanto puntuales como uniformes. Las desigualdades encontradas involucran el módulo de suavidad de alto orden. Aplicamos esta teoría a los operadores singulares trigonométricos.

Let E be a vector valued sequence space with operator valued ß- dual EßY. If E satisfies certain gliding hump assumptions, we show that pointwise bounded subsets of EßY are sequentially equicontinuous. The result is established by considering uniform convergence of the elements in EßY

Suppose E is a vector valued sequence space with operator valued ß-dual EßY . If the space E satisfies certain gliding hump conditions, we consider the connection between pointwise bounded subsets A of EßY and the uniform convergence of the elements of A. For linear operators our results contain results of Li, Wang and Zhong for the spaces c0(X) and lp(X).

In this paper, we study some direct results in simultaneous approximation for a new sequence of linear positive operators <img width=86 height=19 src="../../../../../img/revistas/ruma/v50n1/1a040x.png">of Szãsz-Beta type operators. First, we establish the basic pointwise convergence theorem and then proceed to discuss the Voronovaskaja-type asymptotic formula. Finally, we obtain an error estimate in terms of modulus of continuity of the function being approximated.

A Lavrentiev prox-regularization method for optimal control problems with point-wise state constraints is introduced where both the objective function and the constraints are regularized. The convergence of the controls generated by the iterative Lavrentiev prox-regularization algorithm is studied. For a sequence of regularization parameters that converges to zero, strong convergence of the generated control sequence to the optimal control is proved. Due to the proxcharacter of the proposed regularization, the feasibility of the iterates for a given parameter can be improved compared with the non-prox Lavrentiev-Regularization.