New Fixed Point Theorem for generalized T_F -contractive Mappings and its Application for Solving Some Polynomials

Let (X, d) be a complete metric space. In this paper, we study some new fixed point theorems for generalized T_F -contractive mapping defined on complete metric spaces by using graph closed concept and we proved the existence and uniqueness of a fixed point. These conditions are analogous to Ćirić conditions. In this paper, we compare the two concepts of graph closed and sequentially convergent, and we show that the concept of sequentially convergent is a special case of the concept of graph closed. Also, we provide an counterexample for Dubey et. al. and provide an example in support of our main results. Finally, by using our main results, we present an application to solving some polynomials. Our results, extend several results on the topic in the corresponding literature

Keywords:

Fixed point, contractive mapping, generalized T_F-contractive mapping graph closed,

PDF

___

[1] A. Amini-Harandi, Endpoints of set-valued contractions in metric spaces, Nonlinear Anal., 72 (2010) 132–134.
[2] E. Analouei Adegani and M. Bota, Coupled coincidence point results for mappings without mixed monotone property in partially ordered G-metric spaces, Mathematical Analysis and Convex Optimization, 1 (2020) 93–106.
[3] H. Aydi, E. Karapınar and B. Samet, Remarks on some recent fixed point theorems, Fixed Point Theory and Applications, (2012), 2012:76.
[4] S. Banach, Sur Les Operations Dans Les Ensembles Abstraits et Leur Application Aux Equations Integrales, Fund. Math. 3(1922) 133–181 (French).
[5] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (9) (2002) 531–536.
[6] Lj. B. Ćirić, Generalized contraction and fixed point theorem, Publ. Inst. Math. (Beogard) (N.S.) 12 (26) (1971) 19–26.
[7] B. Djafari Rouhani and Sirous Moradi, Common fixed point of generalized φ-weak contractive multi-valued and single valued mappings, Fixed point theory and Applications, (2010), doi:10.1155/2010/708984.
[8] A. K. Dubey, Urmila Mishra and Rita Pal, New fixed point theorems for tf type contractive conditions, Global Journal of Pure and Applied Mathematics, 13, No. 11 (2017) 529–539.
[9] Mehmet Kir and Hukmi Kiziltunc, Some generalized fixed point theorems in the context of ordered metric spaces, J. Nonlinear Sci. Appl., 8 (2015) 7955–7962.
[10] S. Moradi and D. Alimohammadi, New Extensions of Kannan Fixed-Point Theorem on Complete Metric and Generalized Metric Spaces, Int. Journal of Math. Analysis, 5, No. 47 (2011) 2313–2320.
[11] S. Moradi and A. Beiranvand, Fixed Point of TF − contractive Single-valued Mappings, Iranian Journal of Mathematical Sciences and Informatics, 5, No. 2 (2010),25–32.
[12] S. Moradi, Z. Fathi, E. Analouee, The common fixed point of single-valued generalized φf -weakly contractive mappings, Applied Mathematics Letters, 24 (2011) 771–776.
[13] S. Moradi, F. Khojasteh, Endpoints of multi-valued generalized weak contraction mappings, Nonlinear Analysis, 74 (2011) 2170–2174.
[14] B. E. Rhoades, Two fixed-point theorems for mappings satisfying a general contractive condition of integral type, Int. J. M. and M. since, 63 (2003) 4007–4013.
[15] B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001) 2683–2693.
[16] B. Samet and C. Vetro, An Integral Version of Ćirić’s Fixed Point Theorem, Mediterr. J. Math., (2011), doi: 10.1007/s00009-011-0120-1.
[17] Q. Zhang and Y.song, Fixed point theory for generalized φ-weak contractions, App. Math. Letters, 22 (2009) 75-78.