Quadratic Reverses of the Continuous Triangle Inequality for Bochner Integral of Vector-valued Functions in Hilbert Spaces

Additive Reverses of the Continuous Triangle Inequality for Bochner Integral of Vector-valued Functions in Hilbert Spaces

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.

Reverses of the Continuous Triangle Inequality for Bochner Integral of Vector-valued Functions in Hilbert Spaces

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

Some Reverses of the Continuous Triangle Inequality for Bochner Integral of Vector-valued Functions in Complex Hilbert Spaces

. In [2], the author has extended the above result for Bochner integrals of vectorvalued functions in real or complex Hilbert spaces. If (H ; 〈·, ·〉) is a Hilbert space over K (K = C,R) and f ∈ L ([a, b] ;H), this means that f : [a, b] → H is Bochner measurable on [a, b] and ∫ b a ‖f (t)‖ dt is finite, and there exists a constant K ≥ 1 and a vector e ∈ H, ‖e‖ = 1 such that (1.3) ‖f (t)‖ ≤ K Re ...

Quadratic Reverses of the Triangle Inequality for Bochner Integral in Hilbert Spaces

Reverses of the Triangle Inequality in Banach Spaces

Recent reverses for the discrete generalised triangle inequality and its continuous version for vector-valued integrals in Banach spaces are surveyed. New results are also obtained. Particular instances of interest in Hilbert spaces and for complex numbers and functions are pointed out as well.