Projective surjectivity of quadratic stochastic operators on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math> and its application

A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and distribution of process. The over an infinite space can be identified by continuous mapping (the so-called operator) defined set all probability distributions (which simplex). In present paper, we consider analogue mentioned acting L1-spaces. Main aim paper to investigate projective surjectivity quadratic operators (QSO) measures. To prove main result, study dimensional apply them considered QSO. Furthermore, obtained results are applied existence positive solution some Hammerstein integral equations.