I= SOLUTION OF RANDOM OPERATOR EQUATIONS AND INCLUSIONS
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Title of Thesis
SOLUTION OF RANDOM OPERATOR EQUATIONS AND INCLUSIONS

Author(s)
Mujahid Abbas
Institute/University/Department Details
National College Business Administration And Economics, Lahore
Session
2005
Subject
Economics
Number of Pages
137
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 Bharucha-Reid in 1976 attracted the attention of several mathematicians and gave wings to this theory.

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S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
73.57 KB
2 1 Preliminaries 1
271.51 KB
  1.1 Basic Definitions 1
  1.2 Multivalued Measurable Mappings 5
  1.3 Random Operators And Random Fixed Points 9
  1.4 Random Iterative Procedures 16
  1.5 Random Multivalued Operator And Random Periodic Points 19
3 2 Iterative Procedures For Solutions Of Random Operator Equations
680.22 KB
  2.1 Convergence Of Iterative Algorithms 25
  2.2 Three Step Random Iterative Process 30
  2.3 Equivalence And Stability Of Random Fixed Point Iterative Procedures 43
  2.4 Solution Of Random Operator Equation 56
4 3 Existence Of Random Solution To The Nonlinear Random Multivalued Inclusion
375.9 KB
  3.1 Existence Of Random Periodic Points Of Random Multivalued Operators 94
  3.2 Existence Of Random Fixed Points Of Random Multivalued Operator 100
  3.3 Common Random Fixed Point Of Random R-Multivalued Operators 108
  3.4 Convergence Of Multivalued Measurable Operators 112
  3.5 Coupled Random Fixed Points Of Random Multivalued Operator On Ordered Banach Spaces 118
5 4 References 127
550.52 KB