Keywords and phrases: common fixed point theorems, analogues of Ćirić’s type, non-unique common fixed points, general contractive conditions, Akram-Zafar-Siddiqui contractive inequality condition.
Received: January 17, 2021; Accepted: February 23, 2021: Published: April 2, 2021
How to cite this article: M. O. Olatinwo, Some non-unique common fixed point theorems for ćirić-akram-zafar-siddiqui hybrid type mappings, JP Journal of Fixed Point Theory and Applications 16(1) (2021), 33-65. DOI: 10.17654/FP016010033
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] J. Achari, Results on nonunique fixed points, Publications de L’Institut Mathematique, Nouvelle Serie 26(40) (1978). [2] J. Achari, On the generalization of Pachpatte’s nonunique fixed point theorem, Indian J. Pure Appl. Math. 13(3) (1982), 299-302. [3] R. P. Agarwal, M. Meehan and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, 2004. [4] B. Ahmad and F. U. Rchman, Some fixed point theorems in complete metric spaces, Math. Japon. 36(2) (1991), 239-243. [5] M. Akram, A. A. Zafar and A. A. Siddiqui, A general class of contractions: Acontractions, Novi Sad. J. Math. 38(1) (2008), 25-33. [6] S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math. 3 (1922), 133-181. [7] V. Berinde, Iterative Approximation of Fixed Points, Editura Efemeride, 2002. [8] V. Berinde, Approximating fixed points of weak contractions using Picard iteration, Nonlinear Analysis Forum 9(1) (2004), 43-53. [9] V. Berinde, Iterative Approximation of Fixed Points, Springer-Verlag, Berlin, Heidelberg, 2007. [10] S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci. 10 (1972), 727-730. [11] Lj. B. Ćirić, On contraction type mappings, Math. Balk. 1 (1971), 52-57. [12] Lj. B. Ćirić, On some maps with a nonunique fixed point, Publ. Inst. Math. 17(31) (1974), 52-58. [13] Lj. B. Ćirić, Some recent results in metrical fixed point theory, University of Belgrade, 2003. [14] E. Karapinar, Some nonunique fixed point theorems of Ciric type on cone metric spaces, Abstract and Applied Analysis, 2010, Article ID 123094, 14 pp. [15] D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8(2) (1977), 223-230. [16] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83(4) (1976), 261-263. [17] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 10 (1968), 71-76. [18] M. A. Khamsi and W. A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, John Wiley & Sons, Inc., 2001. [19] A. R. Khan, V. Kumar and N. Hussain, Analytical and numerical treatment of Jungck-type iterative scheme, Appl. Math. Comput. 231 (2014), 521-535. [20] M. O. Olatinwo, Some Banach type fixed point theorems and implicit type error estimates, Kochi J. Math. 8 (2013), 105-117. [21] M. O. Olatinwo, Non-unique fixed point theorems of Ćirićs type for rational hybrid contractions, Journal of Nanjing University Mathematical Biquarterly 31(2) (2014), 140-149. [22] M. O. Olatinwo, Some Ćirićs type non-unique fixed point theorems and rational type contractive conditions, Kochi Journal of Mathematics 10 (2015), 1-9. [23] M. O. Olatinwo, Non-unique fixed point theorems of Achari and Ćirić-Jotic types for hybrid contractions, Journal of Advanced Mathematical Studies 9(2) (2016), 226-234. [24] M. O. Olatinwo, Some non-unique fixed point theorems of Ćirićs type using rational type contractive conditions, Georgian Mathematical Journal 24(3) (2017), 455-461. https://doi.org/10.1515/gmj-2016-0050. [25] M. O. Olatinwo, A new generalization of non-unique fixed point theorems of Ćirić for Akram-Zafar-Siddiqui type contraction, Journal of Mathematical Sciences and Modelling 1(3) (2018), 153-157. https://dx.doi.org/10.33187/jmsm.416632. [26] M. O. Olatinwo, Some generalizations of nonunique fixed point theorems of Ćirićtype for (Φ, Ψ) -hybrid contractive mappings, Annales Mathematicae Silesianae 33 (2019), 221-234. DOI: 10.2478/amsil-2019-0010. [27] B. G. Pachpatte, On Ćirić type maps with a nonunique fixed point, Indian J. Pure Appl. Math. 10(8) (1979), 1039-1043. [28] I. A. Rus, Generalized Contractions and Applications, Cluj Univ. Press, Cluj Napoca, 2001. [29] I. A. Rus, A. Petrusel and G. Petrusel, Fixed point theory, 1950-2000, Romanian contributions, House of the Book of Science, Cluj Napoca, 2002. [30] T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math. 23 (1972), 292-298. [31] E. Zeidler, Nonlinear Functional Analysis and its Applications - Fixed Point Theorems, Springer-Verlag, New York, Inc., 1986.
|