Research on some problems for nonlinear operators (Q838053)

Let \(D\) be a bounded open subset of an infinite-dimensional Menger probabilistic normed space [cf.\ \textit{C.-X.\thinspace Zhu}, ``Several nonlinear operator problems in the Menger PN space'', Nonlinear Anal.,\ Theory Methods Appl.\ 65, No.\,7 (A), 1281--1284 (2006; Zbl 1112.47063)] and \(A:\overline{D}\to E\) a compact continuous operator that satisfies some inequality. Then the author investigates the existence of solutions of an operator equation \(Ax = \mu x\) \((\mu > 1)\) under various inequality conditions.