Algorithm for the generalized Φ-strongly monotone mappings and application to the generalized convex optimization problem



Generalized Φ-strongly monotone, Surjective property, Generalized convex, Optimization


Let E be a uniformly smooth and uniformly convex real Banach space and E∗ be its dual space. We consider a multivalued mapping A : E → 2E∗ which is bounded, generalized Φ-strongly monotone and such that for all t > 0, the range R(Jp+tA) = E∗, where Jp (p > 1) is the generalized duality mapping from E into 2E∗ . Suppose A−1(0) = ∅, we construct an algorithm which converges strongly to the solution of 0 ∈ Ax. The result is then applied to the generalized convex optimization problem.

Author Biographies

M. O. Aibinu, University of KwaZulu-Natal.

School of Mathematics, Statistics and Computer Science.

O. T. Mewomo, University of KwaZulu-Natal.

School of Mathematics, Statistics and Computer Science.


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How to Cite

M. O. Aibinu and O. T. Mewomo, “Algorithm for the generalized Φ-strongly monotone mappings and application to the generalized convex optimization problem”, Proyecciones (Antofagasta, On line), vol. 38, no. 1, pp. 59-82, Feb. 2019.