scholarly journals Implicit Approximation Scheme for the Solution ofK-Positive Definite Operator Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Naseer Shahzad ◽  
Arif Rafiq ◽  
Habtu Zegeye
Keyword(s):  
Error Estimate ◽  
Banach Spaces ◽  
Operator Equation ◽  
Approximation Scheme ◽  
Positive Definite ◽  
Operator Equations ◽  
Definite Operator ◽  
Positive Definite Operator

We construct an implicit sequence suitable for the approximation of solutions ofK-positive definite operator equations in real Banach spaces. Furthermore, implicit error estimate is obtained and the convergence is shown to be faster in comparsion to the explicit error estimate obtained by Osilike and Udomene (2001).

scholarly journals Iterative solutions ofK-positive definite operator equations in real uniformly smooth Banach spaces

2001 ◽  
Vol 27 (3) ◽  
pp. 155-160
Author(s):  
Zeqing Liu ◽  
Shin Min Kang ◽  
Jeong Sheok Ume
Keyword(s):  
Banach Space ◽  
Iterative Method ◽  
Banach Spaces ◽  
Positive Definite ◽  
Operator Equations ◽  
Uniformly Smooth ◽  
Definite Operator ◽  
Iterative Solutions ◽  
Uniformly Smooth Banach Spaces ◽  
Positive Definite Operator

LetXbe a real uniformly smooth Banach space and letT:D(T)⫅X→Xbe aK-positive definite operator. Under suitable conditions we establish that the iterative method by Bai (1999) converges strongly to the unique solution of the equationTx=f,f∈X. The results presented in this paper generalize the corresponding results of Bai (1999), Chidume and Aneke (1993), and Chidume and Osilike (1997).

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