Keywords (Extracted from title, table of contents and abstract of thesis)
random operator equations, iterative algorithms, randomness, nonlinear random systems, nonexpansive random operators, multivalued inclusion 
Abstract The main questions concerning random operator equations are essentially the same as those of deterministic operator equations, that is question of existence, uniqueness, characterization, and constructions and approximations of solutions. The introduction of randomness, however leads to several new questions measurability of solutions, probabilistic and statistical aspects of random solutions, estimate between the mean values of the solutions of the random equations and the deterministic solution of averaged equations etc. The Parague School of probability first initiated the systematic study of random operator equations employing the methods of functional analysis in the 1950s. The study of random fixed point theory is the core around which the theory of random operators has developed. The various ideas associated with random fixed point theory are used to form a particularly elegant approach for the solution of nonlinear random systems (see, [24]). The machinery of random fixed points theory provides a convenient was of modeling many problems arising from economic theory, see for example [95], and references mentioned therein . Spacek and Hans first proved random fixed point theorems for random contraction mappings on separable complete metric space. The survey article by BharuchaReid in 1976 attracted the attention of several mathematicians and gave wings to this theory.
