NEUTROSOPHIC INNER PRODUCT SPACES AND THE CONSTRUCTION OF NEUTROSOPHIC HILBERT SPACES WITH APPLICATION

Abstract

In this paper, a new denition of neutrosophic inner product spaces is proposedunder fewer axiomatic conditions, ensuring consistency with the classical notion of innerproduct spaces. Based on this formulation, several fundamental analytical results are rig-orously established, including convergence theorems, a neutrosophic analogue of Schwarz's inequality, and a precise characterization of orthogonality in neutrosophic inner productspaces. Furthermore, neutrosophic Hilbert spaces are introduced, and a corresponding neu-trosophic form of the Riesz representation theorem is derived. In addition, a number of significant results in fixed point theory are proved and subsequently employed to investigatethe existence and uniqueness of solutions to Uryson's integral equation.