– Weak and Strong Convergence of an Iterative Algorithm for Lipschitz Pseudo-Contractive Maps in Hilbert Spaces –
Download Weak and Strong Convergence of an Iterative Algorithm for Lipschitz Pseudo-Contractive Maps in Hilbert Spaces project materials: This project material is ready for students who are in need of it to aid their research.
ABSTRACT
Let H be a real Hilbert space and K a nonempty, closed convex subset of H.Let T : K → K be Lipschitz pseudo-contractive map with a nonempty fixed points set.
We introduce a modified Ishikawa iterative algorithm for Lipschitz pseudo-contractive maps and prove that our new iterative algorithm converges strongly to a fixed point of T in real Hilbert space.
INTRODUCTION
The contribution of this thesis falls under a branch of mathematics called Functional Analysis.
Functional Analysis as an independent mathematical discipline started at the turn of the 19th century and was finally established in 1920’s and 1930’s, on one hand under the influence of the study of specific classes of linear operators-integral operators.
Integral equations connected with them-and on the other hand under the influence of the purely intrinsic development of modern mathematics with its desire to generalize and thus to clarify the true nature of some regular behaviour.
Quantum Mechanics also had a great influence on the development of Functional Analysis, since its basic concepts, for example energy, turned out to be linear operators on infinite dimensional spaces.
In the early stages of the development of Functional Analysis the problems studied were those that could be stated and solved in terms of linear operators on elements of the space alone.
But as the concept of a space was being developed and deepened, the concept of a function was being developed and generalized. In the end, it became necessary to consider mapping (not necessary linear) from one space into another.
REFERENCES
Y.I. Alber, ”Metric and Generarized Projection Operators in Banach Spaces : prop- erties and applications,” in Theory and Applications of Non linear operators of Accretive and Monotone Type, vol.178 of Lecture Notes in Pure and Applied Math- ematics, pp. 15-50, Marcel Dekker, New York, NY, USA,1996.
Asplund, Positivity of Duality Mappings, Bull. Amer. Math. Soc., 73 (1967), 200-203
Banach, Sur les Operations Dans Les Emsembles Abstraits et Leur Application Aux Equations Integrals. Fundamenta Mathematicae 3, 133-181 (1922).
H.H. Bauschke, J. Borwein, On Projection Algorithms for Solving Convex Feasibility Problems. SIAM Rev. 38, 367-426 (1996).
Berinde, Generalized Contractions and Applications (Romanian), Editura cub press 22, Baiamare, 1997.
Berinde, Iterative Approximation of Fixed Points (Springer, Berlin, 2007).
Borwein and J.M. Bowein, Fixed Point Iterations for Real Functions, J.Math.Anal.Appl. 157(1991), 112-126.
StudentsandScholarship Team.
Be the first to comment