scholarly journals Approximation of a Solution for aK-Positive Definite Operator Equation

1997 ◽  
Vol 210 (1) ◽  
pp. 1-7 ◽  
Author(s):  
C.E. Chidume ◽  
M.O. Osilike
Keyword(s):  
Operator Equation ◽  
Positive Definite ◽  
Definite Operator ◽  
Positive Definite Operator

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 The Solution by Iteration of a Composed K-Positive Definite Operator Equation in a Banach Space

2010 ◽  
Vol 2010 ◽  
pp. 1-7
Author(s):  
S. J. Aneke
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Method Of Moments ◽  
Iterative Scheme ◽  
Inverse Function ◽  
Positive Definite ◽  
Inverse Function Theorem ◽  
Definite Operator ◽  
Fréchet Differentiable ◽  
Positive Definite Operator

The equation , where , with being a K-positive definite operator and being a linear operator, is solved in a Banach space. Our scheme provides a generalization to the so-called method of moments studied in a Hilbert space by Petryshyn (1962), as well as Lax and Milgram (1954). Furthermore, an application of the inverse function theorem provides simultaneously a general solution to this equation in some neighborhood of a point , where is Fréchet differentiable and an iterative scheme which converges strongly to the unique solution of this equation.

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