Journal of Advances in Mathematics and Computer Science

A Theorem for Zeros of Maximal Monotone and Bounded Maps in Certain Banach Spaces

M. A. Onyido

Department of Mathematics, University of Nigeria, Nsukka, Nigeria.

M. O. Uba *

Department of Mathematics, University of Nigeria, Nsukka, Nigeria and African University of Science and Technology, Abuja, Nigeria.

M. I. Uzochukwu

Auburn University, USA.

P. U. Nwokoro

Department of Mathematics, University of Nigeria, Nsukka, Nigeria.

E. E. Otubo

African University of Science and Technology, Abuja, Nigeria and Ebonyi State University, Abakaliki, Nigeria.

*Author to whom correspondence should be addressed.

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Abstract

Let X be a p-uniformly convex and q-uniformly smooth real Banach space with dual space X*. Let T₁ : X → 2^X* and T₂ : X → 2^X* be bounded maximal monotone mappings. An iterative process is constructed and proved to converge strongly to a zero of sum of the two maps.

Keywords: Monotone mapping, maximal monotone mappings, uniformly convex space, uniformly smooth space, strong convergence

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