Fixed Point Results for New Classes of k-Strictly Asymptotically Demicontractive and Hemicontractive Type Multivalued Mappings in Symmetric Spaces

• Published in: Symmetry (Basel) Vol. 16; no. 9; p. 1104
• Main Authors: Agwu, Imo Kalu, Ali, Faeem, Igbokwe, Donatus Ikechi, Ahmad, Iqbal
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-09-2024
• Subjects: Algorithms; Approximation; Asymptotic methods; Control systems; Differential equations; Fixed points (mathematics); Hilbert space; Inequality; Iterative methods; k-strictly asymptotically demicontractive-type and hemicontractive-type multivalued mappings; Mathematical analysis; optimization; Ordinary differential equations; weak and strong convergence; Japan
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym16091104

Fixed point theory is a significant area of mathematical analysis with applications across various fields such as differential equations, optimization, and dynamical systems. Recently, multivalued mappings have gained attention due to their ability to model more complex and realistic problems. ln this work, novel classes of nonlinear mappings called k-strictly asymptotically demicontractive-type and asymptotically hemicontractive-type multivalued mappings are introduced in real Hilbert spaces that are symmetric spaces. In addition, we discuss the weak and strong convergence results by considered modified algorithms, and a demiclosedness property, for these classes of mappings are proved. Several non-trivial examples are demonstrated to validate the newly defined mappings. Consequently, the results and iterative methods obtained in this study improve and extend several known outcomes in the literature.