Article ID: MTJPAM-D-25-00271

Title: Fixed point theorems for Kannan and Chatterjea operators in cone Banach spaces via tri-inertial split-averaged λ-iteration with applications

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-25-00271; Volume 7 / Issue 3 / Year 2025, Pages 130-143

Document Type: Research Paper

Author(s): ‪Elvin Rada ^a

^aDepartment of Mathematics, University of Elbasan “Aleksand\”err Xhuvani”, Ismail Zyma Street No. 1, 3001 Elbasan, Albania

Received: 13 October 2025, Accepted: 14 December 2025, Published: 4 July 2026

Corresponding Author: Elvin Rada (Email address: elvin.rada@uniel.edu.al)

Full Text: PDF

---

Abstract

We establish fixed point theorems for Kannan-type and Chatterjea-type operators in cone Banach spaces using a tri-inertial split-averaged λ-iteration scheme with perturbations. The framework unifies and extends the classical Picard, Mann, and Ishikawa iterations. By employing scalarization through a strictly positive functional, we obtain norm convergence, error estimates, and uniqueness results. Applications to nonlinear differential and integral equations are also presented.

Keywords: Fixed point theorem, Kannan operator, Chatterjea operator, cone Banach space, tri-inertial iteration, λ-iteration, perturbation stability, nonlinear integral equations

References:

1. T. Abdeljawad and E. Karapınar, Quasi-cone metric spaces and generalizations of Caristi–Kirk’s theorem, Fixed Point Theory Appl. 2009, 1–9, 2009; Article ID: 574387, https://doi.org/10.1155/2009/574387.
2. T. Abdeljawad and E. Karapınar, A common fixed point theorem of a Gregus type on convex cone metric spaces, J. Comput. Anal. Appl. 13 (4), 609–621, 2011.
3. T. Abdeljawad, E. Karapınar and K. Taş, Common fixed point theorems in cone Banach spaces, Hacet. J. Math. Stat. 40 (2), 211–217, 2011.
4. V. Berinde, Iterative approximation of fixed points, Springer, Berlin, 2007.
5. S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci. 25 (6), 727–730, 1972.
6. D. Cortild and J. Peypouquet, Krasnosel’skiı̆–Mann iterations: inertia, perturbations and approximation, J. Optim. Theory Appl. 204 (1), 35–60, 2025.
7. W.-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal-Theor. 72 (5), 2259–2261, 2010; DOI: 10.1016/j.na.2009.10.026.
8. W.-S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal-Theor. 73 (5), 1439–1446, 2010; DOI: 10.1016/j.na.2010.05.007.
9. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60, 71–76, 1969.
10. E. Karapınar, Fixed point theorems in cone Banach spaces, Fixed Point Theory Appl. 2009, 1–9, 2009; Article ID: 609281.
11. E. Karapınar, Couple fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl. 59 (12), 3656–3668, 2010.
12. E. Karapınar, Some nonunique fixed point theorems of Ćirić type on cone metric spaces, Abstr. Appl. Anal. 2010, 1–14, 2010; Article ID: 123094, https://doi.org/10.1155/2010/123094.
13. E. Karapınar and W.-S. Du, A note on b-cone metric and its related results: generalizations or equivalence?, Fixed Point Theory Appl. 2013, 2013; Article ID: 210, https://doi.org/10.1186/1687-1812-2013-210.
14. E. Karapınar and A. D. Türkoğlu, Best approximations theorem for a couple in cone Banach space, Fixed Point Theory Appl. 2010, 1–9, 2010; Article ID: 784578, https://doi.org/10.1155/2010/784578.
15. H. Long-Guang and Z. Xian, Cone metric spaces and fixed point theorems, J. Math. Anal. Appl. 332 (2), 1468–1476, 2007.
16. Sh. Rezapour and R. Hamlbarani, Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl. 345 (2), 719–724, 2008.

---

Cite this article