Fixed point curves for linear interpolations of contraction maps

Abstract

Let X be a banach space. If f₀.f₁ :X→X are contraction maps, then for each t in [0,1], let f_t=(1−t)−f₀+t−f₁. This paper is concerned with the analytical properties of the curve of fixed points of the family |f_t:0≤t≤1| and with the question of when, for a map G:[0,1]→X there are contraction maps g₀,g₁ : X→X such that g_t[G(t)]=G(t) for all t in [0,1].

Keywords:

• Contraction maps
• Banach space
• fixed points
• 46B20
• 54E40
• 54H99

AMS(MOS)::

• 46B20
• 54E40
• 54H99