SHAINI P - Academia.edu (original) (raw)
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King AbdulAziz University (KAU) Jeddah, Saudi Arabia
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Let X be a real Banach space, D a bounded open subset of X, and D the closure of D. We prove some... more Let X be a real Banach space, D a bounded open subset of X, and D the closure of D. We prove some fixed point theorems for 1-set contractions and sum of two operators using the Interior Condition. In section 2 of this paper we prove a fixed point theorem for 1-set contractions T : D → X under the interior condition and use it to deduce other theorems. In section 3 we have fixed point results for nonexpansive, lane, and uniformly strictly contractive maps with compact or completely continuous perturbations.
Let X be a real Banach space, D a bounded open subset of X, and D the closure of D. We prove some... more Let X be a real Banach space, D a bounded open subset of X, and D the closure of D. We prove some fixed point theorems for 1-set contractions and sum of two operators using the Interior Condition. In section 2 of this paper we prove a fixed point theorem for 1-set contractions T : D → X under the interior condition and use it to deduce other theorems. In section 3 we have fixed point results for nonexpansive, lane, and uniformly strictly contractive maps with compact or completely continuous perturbations.