Common Fixed Theorems for Generalized (ψ,φ) Weakly Contraction Maps
DOI: 167 Downloads 5374 Views
Author(s)
Abstract
Common fixed point, generalized (ψ,φ) weak contraction, complete metric spaces
Keywords
In this paper, common fixed point theorems of some continuous self-maps under the generalized (ψ,φ) weakly contractions are established in complete metric spaces (X,d). The theorems are proved by subjecting the maps S and T as subspaces of complete metric spaces (f(X),d) and (g(X),d), respectively, and undermining the idea commuting or IT-commuting maps. The results obtained are improvement and unification of some known results as justify with examples. Recent literature are embedded in the present results.
Cite this paper
S. M. Alata, O. T. Wahab, I. F. Usamot,
Common Fixed Theorems for Generalized (ψ,φ) Weakly Contraction Maps
, SCIREA Journal of Mathematics.
Volume 5, Issue 2, April 2020 | PP. 6-21.
References
[ 1 ] | Alata S. M., Rauf K. and Wahab O. T., Some results on common fixed point for generalized f-contraction mapping, Global Journal of Mathematics, 2(1), 99 – 108, 2015. |
[ 2 ] | Alber Y. and Guerre-Delabriere S., Principle of weakly contractive maps in Hilbert spaces. In: Gohlberg, I., Lyubich, Y. (eds) New Results in Operator Theory. Adv. Appl., 722. Birkhauser, Basel, 1997. |
[ 3 ] | Amari M. and Moutawakil D.E., Some new common fixed point theorems under strict contractive conditions, J.math Anal., 270, 181-188, 2002. |
[ 4 ] | Banach, S., Sur les Operations dans les eusembles abstraits et leur application aus equations integrals, Fund. Math., 3, 133-187, 1922. |
[ 5 ] | Berinde V., A Common fixed point theorem for compatible quasi contractive self mappings in metric spaces. Appl. mat. comput, 213, 348-354, 2009. |
[ 6 ] | Borisut P., Kumam P., Gupta V. and Mani N., Generalized (φ; α; β) weak contractions for initial value problems, Mathematics 2019, 7, 266, 2019. |
[ 7 ] | Chandok S., Some common fixed point theorem for generalized f−weakly contractive mappings, J. Appl. Math. Inform., 29(1-2), 257-265, 2011. |
[ 8 ] | Choudhury B. S., Unique fixed point theorem for weakly C-contractive mappings, Kathmandu University J. Sci. Eng. Tech., 5, 6-13, 2009. |
[ 9 ] | Choudhury, B. S., Metiya, N. and Postolache M., A generalized weak contraction principle with applications to coupled coincidence point problems, Fixed Point Theory and Appl., 2013, ID 152., 2013. |
[ 10 ] | Ciric L. B., Fixed point for generalization multivalued contractions, Math. Vesnik, 9(24), 265-272, 1972. |
[ 11 ] | Ciric L. B., A generalization of Banach’s contraction principle, Proc. Amer. math Soc., 45, 267-273, 1974. |
[ 12 ] | Ciric L. B., On a family of contractive maps and fixed points, Institut Mathematique. Publications. Nouvelle Serie, vol. 1731, 4551 pages, 1974. |
[ 13 ] | Doric D., Common fixed point for generalized -weak contraction, Appl. Math. Letters, 22, 1896-1900, 2009. |
[ 14 ] | Doric D. and Lazovic R., Some Suzuki- type fixed point theorem for generalized multivalued mappings and applications, Fixed Point theory. Appl., 2011, 13 pages, 2011. |
[ 15 ] | Dutta P. N. and Choudhury B. S., A generalization of contraction principle in metric spaces., Fixed Point theory. Appl., 2008, Article ID 406368, 8 pages, 2008. |
[ 16 ] | Fei HE, YU-QI Sun, XIAO-YUE Zhao, A common fixed point theorem for generalized -weak contractions of Suzuki type, Journal of Mathematical Analysis, 8(2), 80-88, 2017. |
[ 17 ] | Isufati, A., Rational contractions in b-metric spaces, Journal of Advances in Mathematics, 5, 803-811, 2014. |
[ 18 ] | Jackymski J., Equivalent conditions for generalized contraction on (ordered) metric spaces, Nonlinear Anal., 74, 768-774, 2011. |
[ 19 ] | Jungck G., Commuting mappings and fixed points. Amer. math. monthly, 83, 1976. |
[ 20 ] | Jungck G., Radenovi S., Radojevi, S. and Rakocevic, V, Common fixed point theorems for weakly compatible pairs on cone cetric spaces, Fixed Point Theory and Applications, Vol. 2009, Article ID 643840, 13 pages, 2009. |
[ 21 ] | Khan M.S., Swaleh M. and Sessas, Fixed point theorems by altering distances between the points. Bull.Aust. math. Sco., 30, 1-9, 1984. |
[ 22 ] | Kim K.H, Kang S.M. and Cho Y.J., Common fixed point of φ-contractive mappings, East-Asian math. J., 15, 211-222, 1999. |
[ 23 ] | O¨ ztu¨rk M. and Metin, B., On some common fixed point theorems for f-contraction mappings in cone metric Spaces, Int. Journal of Math. Analysis, 5, 119-127, 2011. |
[ 24 ] | Rauf K. Alata S. M. and Wahab O. T., Common fixed point for generalized five self maps in cone metric spaces, International Journal of Mathematics and Computer Science, 11(2), 199-213, 2016. |
[ 25 ] | Ravindranadh Babu G.V. and Dula Tolera M., Fixed point of generalized -rational contractive mappings α-complete metric spaces, Fasciculi Mathematici, DOI:10.1515/fascmath- 2017-0014 |
[ 26 ] | Reich S., Some remarks concerning contraction mappings, Canad. math. Bull., 14, 121-124, 1971. |
[ 27 ] | Rhoades, B. E., A comparison of various definitions of contractive mappings, American Mathematical Society, 226, 257-290, 1977. |
[ 28 ] | Rhoades, B. E., Some theorems on weakly contractive maps, Nonlinear Analysis, 47, 2683-2693, 2001. |
[ 29 ] | Shyam Lal Singh, Raj Kamal, Se la San M. and Renu Chugh, A fixed point theorem for generalized weak contractions, Faculty of Sciences and Mathematics, University of Nis, Serbia, 1481-1490, 2015. |
[ 30 ] | Vigaya S. and Sucharitha J., Fixed points for four self-mappings in cone metric spaces, International Journal of Mathematical Archive, 5(6), 147 - 152, 2014. |
[ 31 ] | Suzuki T., A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136, 1861-1869, 2008. |
[ 32 ] | Suzuki T., A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71(11), 5313-5317, 2009. |
[ 33 ] | Zhang Q. and Song Y., Fixed point theory for generalized -weak contractions, Applied Mathematics Letters, 22, 75-78, 2009. |