Around averaged mappings
Jarosław Górnicki, Ravindra K. Bisht
Abstract
Abstract This paper is intended for a general mathematical audience. The examples show how the study of existence of fixed points of averaged mappings $$T_{\lambda }= (1-\lambda )I+ \lambda T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>λ</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>I</mml:mi> <mml:mo>+</mml:mo> <mml:mi>λ</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> , where $$0<\lambda <1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>λ</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and I is the identity operator, can help in the study of existence of fixed points of mappings T .