A Constructive Scheme for Tripled Fixed Point Problems in Hilbert Space

Subject Areas : Operation Research

Samuel  Aniki ¹ (Department of Mathematics, Faculty of Science, Confluence University of Science and Technology, Osara, Kogi State, Nigeria)

Received: 2022-05-18 Accepted : 2022-07-19 Published : 2022-06-01

Keywords: Hilbert space, mapping, Mann iterative scheme, tripled fixed point,

Abstract :

Tripled fixed point is an extension to coupled fixed point theory. The idea of tripled fixed point has largely become a focus of research interest in the area of mathematical analysis, especially for their vast application. This research presents a common tripled fixed point iteration for approximating tripled fixed points in linear spaces which is in the context of a Hilbert space. Here, a tripled Mann iterative scheme is defined and applied to resolve the problem of common tripled fixed points of certain mappings. Hence, this work is an extension to recent research in the literature.

References:

Abbas, M., Aydi, H. & Karapınar, E. (2011). Tripled fixed points of multi-valued nonlinear contraction mappings in partially ordered metric spaces. Abstract and Applied Analysis,1-13. Doi:10.1155/2011/812690

Aydi, H. & Karapınar, E. (2012). New Meir-Keeler type tripled fixed point theorems on ordered partial metric spaces. Mathematical Problems in Engineering, 1-17. Doi: 10.1155/2012/409872

Aydi, H., Karapınar, E. & Shatanawi, W. (2012). Tripled fixed point results in generalized metric spaces. Journal of Applied Mathematics, 1-10. Doi:10.1155/2012/314279

Aydi, H., Karapınar, E. & Radenovic, S. (2013). Tripled coincidence fixed point results for Boyd-Wong and Matkowski type contractions. Journal of the Spanish Royal Academy of Sciences, Series A Mathematics, 107, 339-353.

Bhaskar, T.G. & Lakshmikantham, V. (2006). Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Analysis, 65, 1379–1393.

Cheng, R. & Ross, W.T. (2015). Weak parallelogram laws on Banach spaces and applications to prediction. Periodica Mathematica Hungarica,71(1), 45-58. Doi: 10.1007/s10998-014-0078-4.

Choudhury, B.S. & Kundu, S. (2016). A constructive algorithm for a coupled fixed point problem. Nonlinear Funct. Anal. Appl., 21, 567–572.

Dehaish, B.A.I., Khamsi, M.A. & Khan, A.R. (2013). Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces. Journal of Mathematical Analysis and Applications, 397, 861–868.

Karapınar, E., Aydi, H. & Mustafa, Z. (2013). Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces. Tamkang Journal of Mathematics, 44, 233-251.

Kim, K.S. (2019). Convergence theorems of variational inequality for asymptotically nonexpansive nonself mapping in CAT(0) spaces. Mathematics, 7(12), 1234.

Kim, K.S. (2020). A constructive scheme for a common coupled fixed point problems in Hilbert Space. Mathematics. 8(10), 1717.

Lakshmikantham, V. & Ciric, L. (2009). Coupled fixed point theorems for non linear contractions in partially ordered metric spaces. Nonlinear Analysis, 70, 4341–4349.

Luong, N.V. & Thuan, N.X. (2011). Coupled fixed points in partially ordered metric spaces and application. Nonlinear Analysis, 74, 983–992.

Ran, A.C.M. & Reurings, M.C.B. (2004). A fixed point theorem in partially ordered sets and some applications to matrix equations. Proceedings of the American Mathematical Society, 132, 1435–1443.