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Paper   IPM / M / 12734
School of Mathematics
  Title:   Fixed set theorems with application to the fixed point theory
  Author(s):  M. Fakhar (Joint with Z. Soltani and J. Zafarani)
  Status:   Published
  Journal: Journal of Nonlinear and Convex Analysis
  Vol.:  17
  Year:  2016
  Pages:   569--578
  Supported by:  IPM
Here, we show that continuous set-valued maps which are generalized set contraction on noncompact topological spaces have a maximal invariant (fixed) set. As an application, we prove the existence and uniqueness of endpoints for topological contraction mappings. Also, we present fractal set results for system of continuous set-valued maps on regular topological spaces. As application of our result, we show how some fixed point theorems can be established from these results.

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