Some Results on Fixed Point Theorems in Banach Algebras

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Dipankar Das, Nilakshi Goswami, Vishnu Narayan Mishra, Some Results on Fixed Point Theorems in Banach Algebras, Int. J. Anal. Appl., 13 (1) (2017), 32-40.

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Dipankar Das, Nilakshi Goswami, Vishnu Narayan Mishra

Abstract

Let X be a Banach algebra and D be a nonempty subset of X. Let (T 1, T 2) be a pair of self mappings on D satisfying some specific conditions. Here we discuss different situations for existence of solution of the operator equation u = T 1 uT 2 u in D. Similar results are established in case of reflexive Banach algebra X with the subset D. Again, considering a bounded, open and convex subset B in a uniformly convex Banach algebra X with three self mappings T 1 ,T 2 ,T 3 on B, we derive the conditions for existence of solution of the operator equation u = T 1 uT 2 u + T 3 u in B. Application of some of these results to the tensor product is also shown here with some examples.

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