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The theory of fixed points has been revealed as a major, powerful and important tool in the study of nonlinear phenomena. Fixed point theory has been applied in such diverse fields as Differential Equations, Topology, Economics, Biology, Chemistry, Engineering, Game Theory, Physics, Dynamics, Optimal Control, and Functional Analysis. Recent rapid development of efficient techniques for computing fixed points has enormously increased the usefulness of the theory of fixed points for applications. Thus, fixed point theory is increasingly becoming an invaluable tool in the arsenal of the applied mathematics. Many of the most important nonlinear problems of applied Mathematics reduce to solving a given equation which in turn may be reduced to finding the fixed points of a certain operator. Furthermore, contractive-type conditions naturally arise for many of these problems. Thus metrical fixed point theory has developed significantly in the second part of the 20th century. It is this important and dynamic area that have been our main area of research for over two decades now. While majority of our research are in the area of approximation of fixed points of very important operators and solutions of operator equations, and on the stability of iteration procedures, we are also making modest contributions in the area of existence (and uniqueness) of fixed points of certain operators and solutions of operator equations.