Fixed point theorems with various enriched contraction conditions in generalized Banach spaces
Keywords:
Banach space, enriched Kannan, enriched Chatterjea, averaged operator, Krasnoselskij iterativeAbstract
In this paper we introduce some fixed point theorems type contractions on generalized Banach space and we introduce a class of enriched Chatterjea mapping, enriched Kannan contraction mappings, This section is repeated enriched Chatterjea contraction mapping and enriched Kannan and enriched Chatterjea contraction mapping. And we show that these mappings must have unique fixed points in generalized Banach space.
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References
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[5]Berinde, V. and P˘acurar, M., Kannan’s fixed point approximation for solving split feasibility and variational inequality problems, J. Comput. Appl. Math., 386 (2021), 113217, 9 pp.
[6] Berinde, Vasile, and Mădălina Păcurar. "Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative method in Banach spaces." arXiv preprint arXiv:1909.03494 (2019).
[7] Berinde, Vasile, and Mădălina Păcurar. "Approximating fixed points of enriched contractions in Banach spaces." Journal of Fixed Point Theory and Applications 22.2 (2020): 1-10.
[8] Berinde, Vasile, and Mădălina Păcurar. "Kannan’s fixed point approximation for solving split feasibility and variational inequality problems." Journal of Computational and Applied Mathematics 386 (2021): 113217.
[9] Berinde, Vasile, and Mădălina Păcurar. "Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces." Carpathian Journal of Mathematics 37.2 (2021): 173-184.
[10] Bhardwaj, Ramakant, Balaji R. Wadkar, and Basant Singh. "Fixed point theorems in generalized Banach Space." International journal of Computer and Mathematical Sciences (IJCMS), ISSN (2015): 2347-8527.
[11]Chatterjea, S.K. Fixed-point theorems. C. R. Acad. Bulg. Sci. 1972, 25, 727–730. [CrossRef].
[12] D.W. Boyd, T.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969) 458–464.
[13] Goebel, K., Reich, S.: Uniform convexity, hyperbolic geometry, and nonexpansive mappings. In: Monographs and Textbooks in Pure and Applied Mathematics, vol. 83. New York: Marcel Dekker, Inc. (1984).
[14] kannan.R, Some results on fixed points, Bull.Calcutta Math.Soc., 60, 1968, 71-76.
[15]. kannan.R, Some results on fixed points -II, Amer.Math.Monthly, 76, 1969,405-408.
[16] Ramakant B, Balaji R and Basant Z 2015 Fixed Point Theorem in Generalized Banach Space International Journal of Computer & Mathematical Sciences IJCMS Volume 4 p 96-102.
[17] Rus, I.A., Petru¸sel, A., Petru¸sel, G.: Fixed Point Theory. Cluj University Press, Cluj-Napoca (2008).
[18] S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 57 (1975) 194–198.
[19] Zamfirescu, T. Fix point theorems in metric spaces. Arch. Math. 1972, 23, 292–298. [CrossRef].
[20] Zeidler, E.: Nonlinear Functional Analysis and its Applications. I. Fixed-Point Theorems. Springer, New York (1986).
[21] Zeidler, E.: Nonlinear Functional Analysis and its Applications. III. Variational Methods and Optimization. Springer, New York (1985).
[CrossRef]
[2]Berinde, V. Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces. Carpathian J. Math. 2019, 35, 293–304. [CrossRef]
[3]Berinde, V. Approximating fixed points of enriched nonexpansive mappings in Banach spaces by using a retraction-displacement condition. Carpathian J. Math. 2020, 36, 27–34. [CrossRef]
[4] Berinde, V.: Iterative Approximation of Fixed Points. Lecture Notes in Mathematics, vol. 1912, 2nd edn. Springer, Berlin (2007).
[5]Berinde, V. and P˘acurar, M., Kannan’s fixed point approximation for solving split feasibility and variational inequality problems, J. Comput. Appl. Math., 386 (2021), 113217, 9 pp.
[6] Berinde, Vasile, and Mădălina Păcurar. "Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative method in Banach spaces." arXiv preprint arXiv:1909.03494 (2019).
[7] Berinde, Vasile, and Mădălina Păcurar. "Approximating fixed points of enriched contractions in Banach spaces." Journal of Fixed Point Theory and Applications 22.2 (2020): 1-10.
[8] Berinde, Vasile, and Mădălina Păcurar. "Kannan’s fixed point approximation for solving split feasibility and variational inequality problems." Journal of Computational and Applied Mathematics 386 (2021): 113217.
[9] Berinde, Vasile, and Mădălina Păcurar. "Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces." Carpathian Journal of Mathematics 37.2 (2021): 173-184.
[10] Bhardwaj, Ramakant, Balaji R. Wadkar, and Basant Singh. "Fixed point theorems in generalized Banach Space." International journal of Computer and Mathematical Sciences (IJCMS), ISSN (2015): 2347-8527.
[11]Chatterjea, S.K. Fixed-point theorems. C. R. Acad. Bulg. Sci. 1972, 25, 727–730. [CrossRef].
[12] D.W. Boyd, T.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969) 458–464.
[13] Goebel, K., Reich, S.: Uniform convexity, hyperbolic geometry, and nonexpansive mappings. In: Monographs and Textbooks in Pure and Applied Mathematics, vol. 83. New York: Marcel Dekker, Inc. (1984).
[14] kannan.R, Some results on fixed points, Bull.Calcutta Math.Soc., 60, 1968, 71-76.
[15]. kannan.R, Some results on fixed points -II, Amer.Math.Monthly, 76, 1969,405-408.
[16] Ramakant B, Balaji R and Basant Z 2015 Fixed Point Theorem in Generalized Banach Space International Journal of Computer & Mathematical Sciences IJCMS Volume 4 p 96-102.
[17] Rus, I.A., Petru¸sel, A., Petru¸sel, G.: Fixed Point Theory. Cluj University Press, Cluj-Napoca (2008).
[18] S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 57 (1975) 194–198.
[19] Zamfirescu, T. Fix point theorems in metric spaces. Arch. Math. 1972, 23, 292–298. [CrossRef].
[20] Zeidler, E.: Nonlinear Functional Analysis and its Applications. I. Fixed-Point Theorems. Springer, New York (1986).
[21] Zeidler, E.: Nonlinear Functional Analysis and its Applications. III. Variational Methods and Optimization. Springer, New York (1985).
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Published
2022-06-14
How to Cite
khuen, W. N., & Hassan, A. S. (2022). Fixed point theorems with various enriched contraction conditions in generalized Banach spaces. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(2), Math Page 15–26. Retrieved from https://jqcsm.qu.edu.iq/index.php/journalcm/article/view/947
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