Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

We introduce a new iterative scheme with a countable family of nonexpansive mappings for the variational inequality problems in Hilbert spaces and prove some strong convergence theorems for the proposed schemes.

In this paper, first, we introduce the new concept of (complex) 2–Hilbert spaces, that is, we define the concept of 2–inner product spaces with a complex valued 2–inner product by using the 2–norm. Next, we prove some theorems on Schwartz’s inequality, the polarization identity, the parallelogram laws and related important properties. Finally, we give some open problems related to 2–Hilbert spa...