In this study, we introduce a novel generalization of triple integral transforms, which is called general transform. We present the definition new approach and prove main properties related to existence, uniqueness, shifting, scaling, inverse. Moreover, relations between transform other transforms are presented, results partial derivatives convolution theorem established. apply solve some appli...

Some inequalities for the Stieltjes integral and applications in numerical integration are given. The Stieltjes integral is approximated by the product of the divided difference of the integrator and the Lebesgue integral of the integrand. Bounds on the approximation error are provided. Applications for the Fourier Sine and Cosine transforms on finite intervals are mentioned as well.

Following the pioneering work of Schapira, we consider topological Radon-type integral transforms on constructible Z-valued functions using the Euler characteristic as a measure. Contributions include: (1) application of the Schapira inversion formula to target localization and classification problems in sensor networks; (2) extension and application of the inversion formula to weighted Radon t...

AnH-function with complex parameters is defined by aMellin-Barnes type integral. Necessary and sufficient conditions under which the integral defining the H-function converges absolutely are established. Some properties, special cases, and an application to integral transforms are given. 2000 Mathematics Subject Classification. Primary 33C60.