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Results of Approximating Coupled Fixed Point of Kannan Interpolative Contraction Mappings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 14 بهمن 1404 اصل مقاله (354.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.35089.5239 | ||
| نویسندگان | ||
| Kamilu Rauf؛ Afeez Olatunde Oyekanmi* | ||
| Department of Mathematics, University of Ilorin, Ilorin, Nigeria | ||
| تاریخ دریافت: 31 مرداد 1403، تاریخ بازنگری: 18 دی 1403، تاریخ پذیرش: 22 دی 1403 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Coupled Fixed Point؛ Metric Space؛ Interpolative Kannan contraction؛ Complete metric space | ||
| مراجع | ||
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[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. | ||
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