Let <mml:math alttext="$X$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> be a metric space and let <mml:math alttext="$CB\left( X \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mi>B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> denote the closed bounded subsets of <mml:math alttext="$X$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> with the
Hausdorff metric. Given a complete subspace <mml:math alttext="$Y$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi></mml:math> of <mml:math alttext="$CB\left( X \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mi>B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>, two fixed point theorems, analogues of results
in [1], are proved, and examples are given to suggest their applicability in practice.

International Journal of Mathematics and Mathematical Sciences

Point-valued mappings of sets

Abstract

Copyright