O modifikovanim obogaćenim verzijama Browder-Göhde- Kirk teoreme nepokretne tačke

  • Divyanshu Chamoli H.N.B. Garhwal University, Uttarakhand
  • Shivam Rawat Graphic Era (Deemed to be) University
  • Monika Bisht Graphic Era Hill University, Dehradun, India
  • R.C. Dimri H.N.B. Garhwal University, Uttarakhand

Sažetak


In this paper, we propose a modified enriched version of the classical Browder-Göhde-Kirk fixed point theorem in the setting of uniformly convex Banach spaces. Furthermore, we define modified enriched asymptotically nonexpansive mappings and proved some results extending the Goebel-Kirk fixed point theorem for these types of mappings. These findings contribute to the ongoing development of fixed point theory and its applications in nonlinear analysis.

Reference

bibitem[Anjum & Abbas, 2024]{riz} Anjum, R., & Abbas, M. 2024. Remarks on $b$-enriched nonexpansive mappings, arXiv preprint arXiv:2405.07999. Available at: https://doi.org/10.48550/arXiv.2405.07999

bibitem[Berinde, 2019]{ber} Berinde, V. 2019. Approximating fixed points of enriched nonexpansive mappings by Krasnoselskii iteration in Hilbert spaces, textit{Carpathian Journal of Mathematics}, 35(3), pp.293-304. Available at: https://www.jstor.org/stable/26905206

bibitem[Berinde & Pacurar, 2020]{bv1} Berinde, V., & Pacurar, M. 2020. Approximating fixed points of enriched contractions in Banach spaces, textit{Journal of Fixed Point Theory and Applications}, 22, 10. Available at: https://doi.org/10.1007/s11784-020-0769-9

bibitem[Berinde, 2020]{18} Berinde, V. 2020. Approximating fixed points of enriched nonexpansive mappings in Banach spaces by using a retraction-displacement condition, textit{Carpathian Journal of Mathematics}, 36, pp.27-34. Available at: https://www.jstor.org/stable/26898779

bibitem[Browder, 1965]{Brow} Browder, F.E. 1965. Nonexpansive nonlinear operators in a Banach space, textit{Proceedings of the National Academy of Sciences of the USA}, 54, pp.1041-1044. Available at: https://doi.org/10.1073/pnas.54.4.104

bibitem[Dugundji & Granas, 1982]{DJ} Dugundji, J., & Granas, A. 1982. Fixed Point Theory, textit{Monografie Mathematyczne, Polska Akademia Nauk, War-szawa}, 1. ISBN: 0387001735, 9780387001739

bibitem[Goebel & Kirk, 1972]{Kirk} Goebel, K., & Kirk, W. A. 1972. A fixed point theorem for asymptotically nonexpansive mappings, textit{Proceedings of the American Mathematical Society}, 35(1), pp.171-174. Available at: https://doi.org/10.1090/S0002-9939-1972-0298500-3

bibitem[Goebel & Reich, 1984]{Goeb} Goebel, K., & Reich, S. 1984. Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, textit{Series of Monographs and Textbooks in Pure and Applied Mathematics}, Dekker, New York. ISBN: 0824772237.

bibitem[Göhde, 1965]{Ghode} Göhde, D. 1965. Zum Prinzip der kontraktiven Abbildung, textit{Mathematische Nachrichten}, 28, pp.251-258. Available at: https://doi.org/10.1002/mana.19650300312

bibitem[Kirk, 1965]{Kirk} Kirk, W. A. 1965. A fixed point theorem for mappings which do not increase distances, textit{American Mathematical Monthly}, 72, pp.1004-1006. Available at: https://doi.org/10.2307/2313345

bibitem[Matkowski, 2007]{JM2} Matkowski, J. 2007. Remarks on Lipschitzian mappings and some fixed point theorems, textit{Banach Journal of Mathematical Analysis}, 2, pp.237-244. Available at: 10.15352/bjma/1240336222

bibitem[Matkowski, 2022]{JM} Matkowski, J. 2022. A refinement of the Browder–Göhde–Kirk fixed point theorem and some applications, textit{Journal of Fixed Point Theory and Applications}, 24, 70. Available at: https://doi.org/10.1007/s11784-022-00985-2

bibitem[Rawat et al., 2023]{R} Rawat, S., Bartwal, A. & Dimri, R.C. 2023. Approximation and existence of fixed points via interpolative enriched contractions, textit{Filomat}, 37(16), pp.5455-5467. Available at: https://doiserbia.nb.rs/img/doi/0354-5180/2023/0354-51802316455R.pdf

bibitem[Reich, 1976]{RS} Reich, S. 1976. The fixed point property for nonexpansive mappings, I, textit{American Mathematical Monthly}, 83(4), pp.266-268. Available at: https://www.tandfonline.com/doi/pdf/10.1080/00029890.1976.11994096

bibitem[Reich, 1980]{RS1} Reich, S. 1980. The fixed point property for nonexpansive mappings, II, textit{American Mathematical Monthly}, 87, pp.292-294. Available at: https://www.tandfonline.com/doi/pdf/10.1080/00029890.1980.11995019

Objavljeno
2025/12/17
Rubrika
Originalni naučni radovi