The investigation into the extent of approximation of a function through its Fourier series constitutes a critical subject within the realm of mathematical analysis, especially within function spaces such as Besov spaces. This chapter presents an examination of the approximation characteristics of a function situated in a Besov space, employing a summability technique predicated on the triple Euler product. The Euler product approach, which represents an augmentation of traditional summability methodologies, significantly improves the convergence attributes of Fourier series, particularly for functions that display restricted smoothness. Our research predominantly aims to delineate upper limits for the error associated with the approximation of a function within a Besov space, utilizing the method of triple summability as applied to its Fourier series. The Besov space, which serves as a generalization of both Sobolev and Hölder spaces, furnishes a coherent framework for the investigation of function approximation, as it encapsulates intricate regularity characteristics. We exploit the triple Euler product to enhance classical findings related to the convergence and approximation of Fourier series. This study significantly contributes to the expansive domains of approximation theory, Fourier analysis, and summability techniques, offering a novel viewpoint on the significance of Euler-type transformations in improving the convergence of Fourier series. Prospective inquiries could expand these findings to encompass other functional spaces, such as Triebel-Lizorkin spaces, and examine potential implications within applied mathematics and engineering. In the current chapter, I have established a result concerning the degree of approximation of functions within the Besov space by means of the triple Euler product summability approach applied to Fourier series.