More on operator Bellman inequality

Refinements of Aczél-Type Inequality and Their Applications

“…The main purpose of this work is to give new refinements of inequalities (4) and (5). As applications, new refinements of inequalities (6) and 7are also given.…”

“…Aczél's inequality plays a very important role in the theory of functional equations in non-Euclidean geometry. Due to the importance of Aczél's inequality (1), it has received considerable attention by many authors and has motivated a large number of research papers giving it various generalizations, improvements, and applications (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the references therein).…”

Some operator Bellman type inequalities

“…whenever A, B are positive contraction operators, Φ is a unital positive linear map on B(H ) and 0 < p < 1. They also [11] showed the following generalization of the Bellman operator inequality…”

“…where p ≥ 1 and a p 1 − n j=2 a p j > 0 or b p 1 − n j=2 b p j > 0. During the last decades several generalizations, refinements and applications of the Bellman inequality in various settings have been given and some results related to integral inequalities are presented; see [4,11,12,13,16] and references therein.…”

Fuzzy Neural Network Q-Learning Method for Model Disturbance Change: A Deployable Antenna Panel Application

“…The reward value vector r can be obtained based on Equation (24). And then, according to the Bellman optimality theory [26], the time difference error of TD (0) can be described as…”