A new approach to the reduction of multiple integrals to simple ones using Chebyshev's kernels

Purpose – This paper seeks to present an original method for transforming multiple integrals into simple integrals.Design/methodology/approach – This can be done by using α‐dense curves invented by Y. Cherruault and A. Guillez at the beginning of the 1980s.Findings – These curves allow one to approximate the space Rn (or a compact of Rn) with the accuracy α. They generalize fractal curves of Mandelbrobdt. They can be applied to global optimization where the multivariables functional is transformed into a functional depending on a single variable.Practical implications – Applied to a multiple integral, the α‐dense curves using Chebyshev's kernels permit one to obtain a simple integral approximating the multiple integral. The accuracy depends on the choice of α.Originality/value – The paper presents an original method for transforming integrals into simple integrals.