Abstract
Project Number
451-03-65/2024-03/200124
References
- [1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3, 133-181, 1922.
Abstract
Inspired by the well-known result stating that if any iterate of a mapping is a Banach contraction on a complete metric space, then the mapping itself possesses a unique fixed point, we investigate that claim for Kannan contraction but by retaining the left-hand side of the inequality as per the mapping itself. With an additional assumption of k -continuity, the existence and uniqueness of a fixed point is obtained for a new class of contractions, m-Kannan contraction, on a complete metric space. Several examples are given in order to substantiate many theoretical claims such as discontinuity at the unique limit point of the iterative sequence or the ones testifying that this class is wider than the class of Kannan mappings.
Supporting Institution
Ministry of Science, Technological Development and Innovation, Republic of Serbia
Project Number
451-03-65/2024-03/200124
References
- [1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3, 133-181, 1922.
Details
| Primary Language | English |
|---|---|
| Subjects | Operator Algebras and Functional Analysis |
| Journal Section | Mathematics |
| Authors | |
| Project Number | 451-03-65/2024-03/200124 |
| Early Pub Date | January 27, 2025 |
| Publication Date | |
| Submission Date | August 5, 2024 |
| Acceptance Date | October 3, 2024 |
| Published in Issue | Year 2025 Early Access |