Suppose <mml:math alttext="$f:C \to X$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>:</mml:mo><mml:mi>C</mml:mi><mml:mo>&#8594;</mml:mo><mml:mi>X</mml:mi></mml:mrow></mml:math> where <mml:math alttext="$C$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi></mml:math> is a closed subset of <mml:math alttext="$X$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math>. Necessary and sufficient conditions are given for <mml:math alttext="$f$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math> to have a fixed point. All results hold when <mml:math alttext="$X$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> is complete metric space. Several results hold in a much more general setting.

International Journal of Mathematics and Mathematical Sciences

Fixed point theorems for non-self maps I

Abstract

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