On the results of proving the equivalence of $\mathcal{T}$-contractive mappings
محورهای موضوعی : Operator theory
S. S. Karimizad
1
(Department of Mathematics, Faculty of Basic Sciences, Ilam University, Ilam, Iran)
کلید واژه: $\mathcal{T}$-contraction, fixed point, $w$-distance, cone metric space, $\mathfrak{c}$-distance, partial order,
چکیده مقاله :
The main goal of this paper is to compare the proof of the existence and uniqueness of fixed points for $\mathcal{T}$-contractive mappings in various metric spaces and different distances regarding some techniques in mathematical analysis. Also, several comparisons to show the efficiency of the obtained result will be considered.
The main goal of this paper is to compare the proof of the existence and uniqueness of fixed points for $\mathcal{T}$-contractive mappings in various metric spaces and different distances regarding some techniques in mathematical analysis. Also, several comparisons to show the efficiency of the obtained result will be considered.
[1] M. Abbas, V. Parvaneh, A. Razani, Periodic points of T-Ciric generalized contraction mappings in ordered metric spaces, Georgian Math. J. 19 (2012), 597-610.
[2] M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. 22 (4) (2009), 511-515.
[3] H. Aydi, E. Karapınar, B. Samet, Remarks on some recent fixed point theorems, Fixed Point Theory Appl. (2012), 2012:76.
[4] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133-181.
[5] A. Beiranvand, S. Moradi, M. Omid, H. Pazandeh, Two fixed-point theorems for special mappings, arXiv: 0903.1504.
[6] T. Bekeshie, G. A. Naidu, Recent fixed point theorems for T-contrative mappings and T-weak contractions in metric and one metric spaces are not real generalization, JNAO. 4 (2) (2013), 219-225.
[7] K. P. Chi, On a fixed point theorem for certain class of maps satisfying a contractive condition depended on an another function, Lobachevskii J. Math. 30 (4) (2009), 289-291.
[8] L. B. Ciric, A certain class of maps and fixed point theorem, Publ. Inst. Math. 20 (34) (1976), 73-78.
[9] Y. J. Cho, R. Saadati, S. H. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011), 1254-1260.
[10] Z. Fadail, A. Bin Ahmad, Fixed point theorems of T-contraction mappings under c-distance in cone metric spaces, AIP Conf. Proc. 1571 (2013), 1030-1034.
[11] M. Filipovic, L. Paunovic, S. Radenovic, M. Rajovic, Remarks on “Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings”, Math. Comput. Modelling. 54 (2011), 1467-1472.
[12] L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1467-1475.
[13] J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 136 (2008), 1359-1373.
[14] O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon. 44 (1996), 381-391.
[15] J. R. Morales, E. M. Rojas, Cone metric spaces and fixed point theorems of T-contrative mappings, Revista Notas de Matemtica. 4 (2) (2008), 66-78.
[16] J. R. Morales, E. M. Rojas, On the existence of fixed points for contraction mappings depending on two functions, Bull. Iran. Math. Soc. 40 (3) (2014), 689-698.
[17] R. Pal, A. K. Dubey, M. D. Pandey, Fixed point theorems for T-contractions with c-distance on cone metric spaces, J. Inform.. Math. Sci. 11 (3-4) (2019), 265-272.
[18] H. Rahimi, B. E. Rhoades, S. Radenovi´ c, G. Soleimani Rad, Fixed and periodic point theorems for T-contractions on cone metric spaces, Filomat. 27 (5) (2013), 881-888.
[19] H. Rahimi, G. Soleimani Rad, Fixed point theory in various spaces, Lambert Academic Publishing, Germany, 2013.
[20] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435-1443.
[21] B. E. Rhoades, A comparison of various definition of contractive mappings, Trans. Amer. Math. Soc. 266 (1977), 257-290.
[22] W. Sintunavarat, Y. J. Cho, P. Kumam, Common fixed point theorems for c-distance in ordered cone metric spaces, Comput. Math. Appl. 62 (2011), 1969-1978.
[23] F. Yousefi, H. Rahimi, G. Soleimani Rad, A discussion on fixed point theorems of Ciric and Fisher on w-distance, J. Nonlinear Convex Anal. 23 (2022), 1409-1418.
