CONVERGENCE THEOREMS FOR THE ZEROS OF A FINITE FAMILY OF GENERALIZED ACCRETIVE OPERATORS

Volume 2, Issue 4, pp 260-269 http://dx.doi.org/10.22436/jnsa.002.04.08

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Authors

N. GURUDWAN - School of Studies in Mathematics, Pt. Ravishankar Shukla University Raipur - 492010 (C.G.), India. B. K. SHARMA - School of Studies in Mathematics, Pt. Ravishankar Shukla University Raipur - 492010 (C.G.), India.

Abstract

A strong convergence theorem for the common zero for a finite family of Generalized Lipschitz operators in a uniformly smooth Banach space is proved when atleast one of the operator is Generalized \(\Phi\)- accretive, using a new iteration formula. Similar result for Generalized Lipschitz and Generalized \(\Phi\)- pseudocontractive map is also proved. Our result extends the convergence results of Chidume [4] to a finite family improving many other results.

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Keywords

• Generalized \(\Phi\)-accretive
• generalized Lipschitz
• uniformly smooth Banach space
• mann iteration.

MSC

•  47H06
•  47H09

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