We study the antieigenvectors of the generalized eigenvalue problem Af = λBf by using the concept of stationary vectors and then obtain an operator inequality complementary to Schwarz’s inequality in Hilbert space. AMS Mathematics Subject Classification (2000): 47A63,47A75

Some new refinements of the Schwarz inequality in inner product spaces are given. Applications for discrete and integral inequalities including the Heisenberg inequality for vectorvalued functions in Hilbert spaces are provided.

In this paper, by introducing some parameters and by employing a sharpening of Hölder’s inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder’s theorem is given.

Some new reverses of the Cauchy-Bunyakovsky-Schwarz integral inequality for vector-valued functions in Hilbert spaces that complement the recent results obtained in [1] are given. Applications for the Heisenberg inequality are provided.

‎in a real hilbert space‎, ‎an iterative scheme is considered to‎ ‎obtain strong convergence which is an essential tool to find a‎ ‎common fixed point for a countable family of nonexpansive mappings‎ ‎and the solution of a variational inequality problem governed by a‎ ‎monotone mapping‎. ‎in this paper‎, ‎we give a procedure which results‎ ‎in developing shehu's result to solve equilibrium prob...

In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.