Operator inequality implying generalized Bebiano–Lemos–Providência one

Antieigenvectors of the Generalized Eigenvalue Problem and an Operator Inequality Complementary to Schwarz’s Inequality

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

An Operator Extension of Bohr's inequality

An Operator Inequality Related to Jensen’s Inequality

For bounded non-negative operators A and B, Furuta showed 0 ≤ A ≤ B implies A r 2BA r 2 ≤ (A r 2BA r 2 ) s+r t+r (0 ≤ r, 0 ≤ s ≤ t). We will extend this as follows: 0 ≤ A ≤ B ! λ C (0 < λ < 1) implies A r 2 (λB + (1− λ)C)A r 2 ≤ {A r 2 (λB + (1 − λ)C)A r 2 } s+r t+r , where B ! λ C is a harmonic mean of B and C. The idea of the proof comes from Jensen’s inequality for an operator convex functio...

On generalized Hermite-Hadamard inequality for generalized convex function

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

One Operator, One Landscape

The use of the term \landscape" is increasing rapidly in the eld of evolutionary computation, yet in many cases it remains poorly, if at all, deened. This situation has perhaps developed because everyone grasps the imagery immediately, and the questions that would be asked of a less evocative term do not get asked. This paper presents an important consequence of a new model of landscapes. The m...