A Comparative Analysis of Fixed Point Results in Banach and Hilbert Spaces

The main objective of this paper is to use contraction mapping and non-expansive operators for unique fixed point results in real Banach and Hilbert spaces. A fundamental role of the fixed point theory plays in optimization and nonlinear functional analysis. This work is a generalization of the unique fixed point and its discussion. We have collected different ideas for unique fixed points in real Banach and Hilbert spaces. Also, we formulate and compare fixed point conditions involving contractive inequalities, the role of completeness, nom structure,inner product geometry, lower semicontinuous auxiliary function and Hausdorff distance for set valuede maps. Finally, we have conducted a comparative study and analysis of unique fixed points in Banach and Hilbert spaces. New comparative study, observation, differences analysis and implementation of these structure features are also provided.

Normed space, Banach space, Hilbert space, inner product, unique fixed point, contraction mapping , non-expansive mapping

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