Approximating Fixed Point of Generalized C-class Contractivity Conditions
Keywords:
Fixed Point, C−Class Function, C-Class Akram Contraction, C-Class Generalized MJ−Contraction
Abstract
In this study, we introduced novel class of contractivity conditions called C-class Akram contraction and C-class generalized MJ−Contraction and established the convergence of Picard and Jungck iterations to the unique fixed point and unique common fixed point respectively. Our results generalizes and extends some existing related results in literature.
References
[1] Banach, S.; Sur les Operations dans les Ensembles Abstraits et leur Appliication aux quations intrales, Fundamenta Mathematicae 3, (1922) 133-181.
[2] Akram, M., Zafar, A. A. and Siddiqui, A. A.; A general class of contractions; A-contractions, Novi Sad J. Math., 38. No1(2008), 25-33.
[3] Kannan, R.; Some results on fixed points. Bull Calcutta Math. Soc. 10, (1968) 71-76.
[4] Rakotch, E.; A note on contractive mappings, Proc. Amer Math. Soc. 13, (1962) 459-465.
[5] Reich S.; Kannarfs fixed point theorem, Bull. Univ. Mat. Italiana, (4) 4, (1971) 1-11.
[6] Jungck, G.; Commuting mappings and fixed points, Amer. Math. Monthly, 83, (1976) 261-263.
[7] Olatinwo, M. O. and Omidire, O. J.; Convergence of Jungck-Schaefer and Jungck-Kirk-Mann
iterations to the unique common fixed point of Jungck generalized pseudo-contractive and
Lipschitzian type mappings, Journal of Advanced Math. Stud. 14(1), (2021).
[8] Omidire O. J.; Common Fixed Point of Some Certain generalized Contractive Conditions in Convex Metric Space Settings, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(3), (2024) Pages 1 - 9. https://doi.org/10.5281/zenodo.13152753
[9] Olatinwo, M. O. and Omidire, O. J.; Fixed point theorems of Akram-Banach type, Nonlinear Analysis Forum 21(2), (2016) 55-64.
[10] Olatinwo, M. O. and Omidire, O. J.; Convergence results for Kirk-Ishikawa and some other iterative algorithms in arbitrary Banach space setting, Transactions on Mathematical Programming and Applications, Vol 8, No. 1, (2020) 01-11.
[11] Olatinwo, M. O. and Omidire, O. J.; Some new convergence and stability results for Jungck generalized pseudo-contractive and Lipschitzian type operators using hybrid iterative techniques in the Hilbert spaces. Springer Journals; Rendiconti del Circolo Matematico di Palermo Series 2. (2022)
[12] Singh, S. L., Bhatnagar, C., Mishra, S. N.; Stability of Jungck-type iterative procedures. International J. Math. Sci. 19, (2005) 3035-3043.
[13] Akewe, H.; The Statbility of a Modified Jungck-Mann Hybrid Fixed Point Iteration Procedure, International Journal of Mathematical Sciences and Optimization: Theory and Applications, Vol.1, (2016), pp. 95-104.
[14] Ansari, A.H.; Note on" φ − ψ−contractive type mappings and related fixed point", The 2nd Regional Conference on Mathematics And Applications, PNU, 377-380 (2014).
[15] Khan,M.S., Swaleh, M. and Sessa, S.; Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30(1) (1984), 1-9.
[16] Chuadchawna, P., Chuadchawna, Kaewcharoen, A. and Plubtieng, S.; Fixed point theorems for generalized α−µ−ψ-Geraghty contraction type mappings in α−µ−complete metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 471-485.
[17] Alexandra M., Common fixed point theorems for enriched Jungck contractions in Banach spaces. J. Fixed Point Theory Appl., (2021), https://doi.org/10.1007/s11784-021-00911-y
[18] Jungck, G., Compatible mappings and common fixed points, Int. J. Math. and Math Sci., 9(1986), 771 - 773
[2] Akram, M., Zafar, A. A. and Siddiqui, A. A.; A general class of contractions; A-contractions, Novi Sad J. Math., 38. No1(2008), 25-33.
[3] Kannan, R.; Some results on fixed points. Bull Calcutta Math. Soc. 10, (1968) 71-76.
[4] Rakotch, E.; A note on contractive mappings, Proc. Amer Math. Soc. 13, (1962) 459-465.
[5] Reich S.; Kannarfs fixed point theorem, Bull. Univ. Mat. Italiana, (4) 4, (1971) 1-11.
[6] Jungck, G.; Commuting mappings and fixed points, Amer. Math. Monthly, 83, (1976) 261-263.
[7] Olatinwo, M. O. and Omidire, O. J.; Convergence of Jungck-Schaefer and Jungck-Kirk-Mann
iterations to the unique common fixed point of Jungck generalized pseudo-contractive and
Lipschitzian type mappings, Journal of Advanced Math. Stud. 14(1), (2021).
[8] Omidire O. J.; Common Fixed Point of Some Certain generalized Contractive Conditions in Convex Metric Space Settings, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(3), (2024) Pages 1 - 9. https://doi.org/10.5281/zenodo.13152753
[9] Olatinwo, M. O. and Omidire, O. J.; Fixed point theorems of Akram-Banach type, Nonlinear Analysis Forum 21(2), (2016) 55-64.
[10] Olatinwo, M. O. and Omidire, O. J.; Convergence results for Kirk-Ishikawa and some other iterative algorithms in arbitrary Banach space setting, Transactions on Mathematical Programming and Applications, Vol 8, No. 1, (2020) 01-11.
[11] Olatinwo, M. O. and Omidire, O. J.; Some new convergence and stability results for Jungck generalized pseudo-contractive and Lipschitzian type operators using hybrid iterative techniques in the Hilbert spaces. Springer Journals; Rendiconti del Circolo Matematico di Palermo Series 2. (2022)
[12] Singh, S. L., Bhatnagar, C., Mishra, S. N.; Stability of Jungck-type iterative procedures. International J. Math. Sci. 19, (2005) 3035-3043.
[13] Akewe, H.; The Statbility of a Modified Jungck-Mann Hybrid Fixed Point Iteration Procedure, International Journal of Mathematical Sciences and Optimization: Theory and Applications, Vol.1, (2016), pp. 95-104.
[14] Ansari, A.H.; Note on" φ − ψ−contractive type mappings and related fixed point", The 2nd Regional Conference on Mathematics And Applications, PNU, 377-380 (2014).
[15] Khan,M.S., Swaleh, M. and Sessa, S.; Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30(1) (1984), 1-9.
[16] Chuadchawna, P., Chuadchawna, Kaewcharoen, A. and Plubtieng, S.; Fixed point theorems for generalized α−µ−ψ-Geraghty contraction type mappings in α−µ−complete metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 471-485.
[17] Alexandra M., Common fixed point theorems for enriched Jungck contractions in Banach spaces. J. Fixed Point Theory Appl., (2021), https://doi.org/10.1007/s11784-021-00911-y
[18] Jungck, G., Compatible mappings and common fixed points, Int. J. Math. and Math Sci., 9(1986), 771 - 773
Published
2025-01-03
How to Cite
Omidire, O. J., Ansari, A. H., Ariyo, R. D., & Aduragbemi, M. (2025). Approximating Fixed Point of Generalized C-class Contractivity Conditions. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(1), 1-10. Retrieved from http://ijmso.unilag.edu.ng/article/view/2453
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