The Extension of Some Results on Fixed Points in Abstract Spaces.

      Аннотация: In the first chapter we introduced fixed point,fixed point theory and its applications.In chapters two and three we prove some random fixed point theorems for contractive and expansive type mappings in Hilbert space.In the chapter four we present some common fixed point theorems for rational and other inequalities involving expansive type mappings in Hilbert space.In chapter five we generalize and unify the results of Hardy and Rogers using asymptotically regular maps and sequence.In chapter six results of fixed point in an e–chainable metric space have been established and for this we have used general contractive conditions.In chapter seven we prove the chainability of points and sets is a product invariant property and finally a fixed point theorem is proved.In chapter eight we define asymptotically regular maps and sequence in cone metric spaces and the existence of fixed points for asymptotically regular maps on cone metric spaces is investigated.In chapter nine the existence of fixed point for continuous maps on dislocated metric spaces is investigated.In the last chapter we define Pseudo-2-metric spaces and Pseudo-2-metric product spaces.

Ключевые слова: fixed point, Random fixed point, metric space, Hilbert space, Cone metric space, Random operators, Expansive type mapping, Asymptotically regular maps and sequence, Chainable metric space, Metric product space, Dislocated metric space, Pseudo 2-metric space and Pseudo 2-metric product space.