The Method of Differentiating under the Integral Sign

an 2 00 1 Necessary and sufficient conditions for differentiating under the integral sign

a f(x, y) dy, it is often important to know when F is differentiable and when F (x) = ∫ b a f1(x, y) dy. A sufficient condition for differentiating under the integral sign is that ∫ b a f1(x, y) dy converges uniformly; see [6, p. 260]. When we have absolute convergence, the condition |f1(x, y)| ≤ g(y) with ∫ b a g(y) dy < ∞ suffices (Weierstrass M-test and Lebesgue Dominated Convergence). If we...

Differentiating Under the Integral Sign

Necessary and Sufficient Conditions for Differentiating under the Integral Sign

Spectral Scheme for Solving Fuzzy Volterra Integral Equations of First Kind

This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics ...

The 2-additive fuzzy Choquet integral-based TODIM method with improved score function under hesitant fuzzy environment

Recently, the TODIM$^1$(an acronym in Portuguese of interactive and multi-criteria decision making) method has attracted increasing attention and many researchers have extended it to deal with multiple attribute decision making (MADM) problems under different situations. However, none of them can be used to handle MADM problems with positive, independent, and negative interactions among attribu...