Irfan Ul-haq

Fixed Point Theorems for Pseudo-Contractive Mappings in Banach Spaces

Let X be a Banach space, X* its dual and JX → X* be an duality mapping. Suppose T is any self-mapping on X which satisfies

<(I − T)x − (I − T)y> ≥ 0 for all xy ∈ X.

Then we say T is pseudo-contractive.

We have established sufficient conditions for the existence of a fixed point for continuous pseudo-contractive mappings defined on a subset D of a Banach space X under the following boundary condition:

There is z ∈ D so that Tx − z ≠ λ(x − z) for x ∈ D, λ > 1.