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3: Paper Source PDF document

Paper's Title:

Pseudomonotonicity and Quasimonotonicity by Translations versus Monotonicity in Hilbert Spaces


George Isac and Dumitru Motreanu

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

Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France.


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


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

1Department of Mathematics and Computer Science,
Ebonyi State University, Abakaliki,

2School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.


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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