Abstract
In this paper, equivalence between the Mann and Ishikawa iterations for a generalized contraction mapping in cone subset of a real Banach space is discussed.
Highlights
The iteration techniques of W.R.Mann [1] and Shiro Ishikwa [2] are used to find the approximation of fixed point of a contraction mapping
We see the equivalence between these Mann and Ishikawa iterations for a generalized contraction mapping in a cone
Definition 1.1: Let E be a real Banach space and a subset P of E is said to be a cone if satisfies the following: 1) P, P is closed and P {0} ; 2) ax by P for every x, y P and a,b 0 ; 3) P ( P) = {0}
Summary
The iteration techniques of W.R.Mann [1] and Shiro Ishikwa [2] are used to find the approximation of fixed point of a contraction mapping. Equivalence between the Mann and Ishikawa iterations for a generalized contraction mapping in cone subset of a real Banach space is discussed. We see the equivalence between these Mann and Ishikawa iterations for a generalized contraction mapping in a cone.
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