International Journal of Nonlinear Analysis and Applications
Results of Approximating Coupled Fixed Point of Kannan Interpolative Contraction Mappings
Document Type : Research Paper
Authors
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Abstract
This paper presents the results of approximating coupled fixed point of kannan interpolative contraction mappings. Let $X$ be a complete metric space and $T:X\times X \to X$ be a coupled mapping. We proved the existence and uniqueness of a fixed point theory using coupled interpolative Kannan contractions. We also proved the stability of the interpolative Kannan contraction to validate the well-posedness of the conditions. Our results extend some results in the literature.
Keywords
[1] S.A. Aniki, M.O. Ajisope, M. Raji, and F. Adegboye, Coupled fixed points theorem for mappings satisfying a contractive condition of integral type in Cauchy spaces, FUOYE J. Engin. Technol. 7 (2022), no.3, 1–10.
[2] V. Berinde and M. Pacurar, Coupled fixed point theorems in partially ordered metric spaces and application, J. Nonlinear Convex Anal. 18 (2017), no. 4, 651–659.
[3] T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal.: Theory, Meth. Appl. 65 (2006), no. 7, 1379–1393.
[4] M.F. Bota, L. Guran, and G. Petrusel, Fixed points and coupled fixed points in b-metric spaces via graphical contractions, Carpath. J. Math. 39 (2023), no. 1, 85–94.
[5] D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Carpath. J. Math. 11 (1987), no. 5, 623–632.
[6] H.A. Hammad and M. Zayed, New generalized contractions by employing two control functions and coupled fixed-point theorems with applications, Mathematics 10 (2022), no. 17, 3208.
[7] E. Karapinar, Revisiting the Kannan type contractions via interpolation, Adv. Theory Nonlinear Anal. Appl. 2 (2018), no. 2, 85–87.
[8] R. Kannan, Some results on fixed points-II, Amer. Math. Month. 76 (1969), no. 4, 405–408.
[9] E. Karapinar, Interpolative Kannan-Meir-Keeler type contraction, Adv. Theory Nonlinear Anal. Appl. 5 (2021), no. 4, 611–614.
[10] X.I. Liu, M. Zhou, and B. Damjanovic, Common coupled fixed point theorem for Geraghty-type contraction in partially ordered metric spaces, J. Funct. Spaces 2018 (2018), no. 4, 11–14.
[11] M. Olatinwo and K. Tijani, Some results on the continuous dependence of couple fixed points in a complete metric space, Eur. J. Math. Appl. 2 (2022), 6.
[12] V. Opoitsev, Heterogeneous and combined concave operators, Sib. Math. J. 16 (1975), no. 4, 597–605.
[13] K. Rauf and A.O. Oyekanmi, Results of coupled iterative fixed point approximation, Ann. Math. Comput. Sci. 20 (2024), no. 1–3, 1–13.
[2] V. Berinde and M. Pacurar, Coupled fixed point theorems in partially ordered metric spaces and application, J. Nonlinear Convex Anal. 18 (2017), no. 4, 651–659.
[3] T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal.: Theory, Meth. Appl. 65 (2006), no. 7, 1379–1393.
[4] M.F. Bota, L. Guran, and G. Petrusel, Fixed points and coupled fixed points in b-metric spaces via graphical contractions, Carpath. J. Math. 39 (2023), no. 1, 85–94.
[5] D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Carpath. J. Math. 11 (1987), no. 5, 623–632.
[6] H.A. Hammad and M. Zayed, New generalized contractions by employing two control functions and coupled fixed-point theorems with applications, Mathematics 10 (2022), no. 17, 3208.
[7] E. Karapinar, Revisiting the Kannan type contractions via interpolation, Adv. Theory Nonlinear Anal. Appl. 2 (2018), no. 2, 85–87.
[8] R. Kannan, Some results on fixed points-II, Amer. Math. Month. 76 (1969), no. 4, 405–408.
[9] E. Karapinar, Interpolative Kannan-Meir-Keeler type contraction, Adv. Theory Nonlinear Anal. Appl. 5 (2021), no. 4, 611–614.
[10] X.I. Liu, M. Zhou, and B. Damjanovic, Common coupled fixed point theorem for Geraghty-type contraction in partially ordered metric spaces, J. Funct. Spaces 2018 (2018), no. 4, 11–14.
[11] M. Olatinwo and K. Tijani, Some results on the continuous dependence of couple fixed points in a complete metric space, Eur. J. Math. Appl. 2 (2022), 6.
[12] V. Opoitsev, Heterogeneous and combined concave operators, Sib. Math. J. 16 (1975), no. 4, 597–605.
[13] K. Rauf and A.O. Oyekanmi, Results of coupled iterative fixed point approximation, Ann. Math. Comput. Sci. 20 (2024), no. 1–3, 1–13.
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Articles in Press, Corrected Proof
Available Online from 03 February 2026
- Receive Date: 21 August 2024
- Revise Date: 07 January 2025
- Accept Date: 11 January 2025