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3: Paper Source PDF document

Paper's Title:

Pseudomonotonicity and Quasimonotonicity by Translations versus Monotonicity in Hilbert Spaces

Author(s):

George Isac and Dumitru Motreanu

Department of Mathematics, Royal Military College of Canada, P.O. Box 17000 Stn Forces
Kingston, Ontario, Canada, K7k 7b4.
gisac@juno.com

Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France.
motreanu@univ-perp.fr

Abstract:

Let  be a Gâteaux differentiable mapping on an open convex subset  of a Hilbert space. If there exists a straight line  such that  is pseudomonotone for any  then  is monotone. Related results using a regularity condition are given.



1: Paper Source PDF document

Paper's Title:

Iterative Algorithm for Split Generalized Mixed Equilibrium Problem Involving Relaxed Monotone Mappings in Real Hilbert Spaces

Author(s):

1U.A. Osisiogu, F.L. Adum, and 2C. Izuchukwu

1Department of Mathematics and Computer Science,
Ebonyi State University, Abakaliki,
Nigeria.
E-mail: uosisiogu@gmail.com, adumson2@yahoo.com

2School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: izuchukwuc@ukzn.ac.za, izuchukwu_c@yahoo.com

Abstract:

The main purpose of this paper is to introduce a certain class of split generalized mixed equilibrium problem involving relaxed monotone mappings. To solve our proposed problem, we introduce an iterative algorithm and obtain its strong convergence to a solution of the split generalized mixed equilibrium problems in Hilbert spaces. As special cases of the proposed problem, we studied the proximal split feasibility problem and variational inclusion problem.


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