Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 1, pp. 45-51 (2004)

Iterative Convergence of Resolvents of Maximal Monotone Operators Perturbed by the Duality Map in Banach Space

Safeer Hussain Khan

GIK Institute of Engineering Sciences and Technology, Pakistan

Abstract: For a maximal monotone operator $T$ in a Banach space an iterative solution of $0\in Tx$ has been found through weak and strong convergence of resolvents of these operators. Identity mapping in the definition of resolvents has been replaced by the duality mapping. Solution after finite steps has also been established.

Keywords: Resolvent, maximal monotone operator, weak convergence, strong convergence, iteration scheme.

Classification (MSC2000): 47H05; 49M05

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