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A general fixed point theorem
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In this paper we prove a theorem which ensures the existence of a unique
fixed point and is applicable to contractive type mappings as well as
mappings which do not satisfy any contractive type condition. Our theorem
contains the well known fixed point theorems respectively due to Banach,
Kannan, Chatterjea, Ciric and Suzuki as particular cases; and is
independent of Caristi?s fixed point theorem. Moreover, our theorem provides
new solutions to Rhoades problem on discontinuity at the fixed point as it
admits contractive mappings which are discontinuous at the fixed point. It
is also shown that the weaker form of continuity employed by us is a
necessary and sufficient condition for the existence of the fixed point.
National Library of Serbia
Title: A general fixed point theorem
Description:
In this paper we prove a theorem which ensures the existence of a unique
fixed point and is applicable to contractive type mappings as well as
mappings which do not satisfy any contractive type condition.
Our theorem
contains the well known fixed point theorems respectively due to Banach,
Kannan, Chatterjea, Ciric and Suzuki as particular cases; and is
independent of Caristi?s fixed point theorem.
Moreover, our theorem provides
new solutions to Rhoades problem on discontinuity at the fixed point as it
admits contractive mappings which are discontinuous at the fixed point.
It
is also shown that the weaker form of continuity employed by us is a
necessary and sufficient condition for the existence of the fixed point.
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