
تعداد نشریات | 21 |
تعداد شمارهها | 610 |
تعداد مقالات | 9,029 |
تعداد مشاهده مقاله | 67,082,934 |
تعداد دریافت فایل اصل مقاله | 7,656,390 |
On complex valued $G_b$-metric spaces and related fixed point theorems | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 60، دوره 12، شماره 1، مرداد 2021، صفحه 748-760 اصل مقاله (373.03 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.1448.1366 | ||
نویسندگان | ||
Chakkrid Klin-eam* 1؛ Cholatis Suanoom2 | ||
1Department of Mathematics Faculty of Science Naresuan University, Thailand | ||
2Science and Applied Science Center, Kamphaengphet Rajabhat University, Kamphaengphet, 62000, Thailand | ||
تاریخ دریافت: 26 خرداد 1395، تاریخ بازنگری: 12 آبان 1396، تاریخ پذیرش: 26 آبان 1398 | ||
چکیده | ||
In this paper, we establish complex valued $G_b$-metric spaces and introduced the notion of $G_b$-Banach Contraction, $G_b$-Kannan mapping and prove fixed point theorems in the such spaces. | ||
کلیدواژهها | ||
Fixed point؛ complex valued $G_b$-metric spaces؛ complex valued G-metric spaces؛ G-metric spaces؛ $G_b$-metric spaces؛ $G_b$-Banach contraction and $G_b$-Kannan mapping | ||
مراجع | ||
[1] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations inte´grales, Fund. Math. 3 (1922) 133–181. [2] R. Kannan, Some results on fixed points-II, Amer. Math. Month. 76 (1969) 405–408. [3] A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric spaces, Number. Funct. Anal. Optim. 32 (2011), 243–253. [4] C. Klin-Eam and C. Suanoom, Some common fixed-point theorems for generalized-contractive-type mappings on Complex-Valued Metric Spaces, Abstr. Appl. Anal. 2013 (2013), Article ID 604215, 6 pages. [5] W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Ineq. Appl. 84 (2012). [6] F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl. 64 (2012) 1866–1874. [7] I.A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal. 30 (1989) 26–37. [8] M.H. Shah and N. Hussain, Nonlinear contractions in partially ordered quasi b-metric spaces, Commun. Korean Math. Soc. 27(1) (2012) 117-128. [9] M.A. Alghamdi, N. Hussain, and P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Ineq. Appl. 402 (2013). [10] C.X. Zhu, C.F. Chen, and X. Zhang, Some results in quasi-b-metric-like spaces, J. Ineq. Appl. 437 (2014). [11] C. Klin-Eam and C. Suanoom, Dislocated quasi-b-metric spaces and fixed point theorems for cyclic contractions, Fixed Point Theory Appl. 74 (2015). [12] K. Rao, P. Swamy, and J. Prasad, A common fixed point theorem in complex-valued b-metric spaces, Bull. Math. Stat. Res. 1(1) (2013) 1–8. [13] S. Ghaler, 2-metrische raume und ihre topologische strukture, Math. Nachr. 26 (1963) 115–148. [14] B.C. Dhage, Generalized metric space and mapping with fixed point, Bull. Cal. Math. Soc. 84 (1992) 329–336. [15] R.P. Agarwal and E. Karapinar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed Point Theo. Appl. 2013 (2013). [16] Z. Mustafa and B. Sims, Some remarks concerning D-metric spaces, in Proc. Inter. Conf. Fixed Point Theo. Appl. Valencia, Spain, July 2004, pp. 189–198. [17] Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theo. Appl. 2009 (2009), Article ID 917175, 10 pages [18] Z. Mustafa, A new structure for generalized metric spaces-with applications to fixed point theory, Ph.D. Thesis, The University of Newcastle, Callaghan, Australia, 2005. [19] Z. Mustafa and H. Obiedat, A fixed points theorem of Reich in G-metric spaces, Cubo Math. J. 12(1) (2010) 83–93. [20] Z. Mustafa, F. Awawdeh and W. Sahanawi, Fixed point theorem for expansive mappings in G-metric spaces, Int. J. Contemp. Math. Sci. 5(50) (2010) 2463–2472. [21] A. Aghajani, M. Abbas and J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces, Filomat, in press. [22] S. M. Kang, B. Singh, V. Gupta and S. Kumar, Contraction principle in complex-valued G-Metric spaces, Int. J. Math. Anal. 7 (2013) 2549–2556. [23] C. Klin-eam and C. Suanoom, Dislocated quasi-b-metric spaces and fixed point theorems for cyclic contractions, Fixed Point Theory Appl. 74 (2015). [24] C. Klin-eam, C. Suanoom and S. Suantai, Generalized multi-valued mappings satisfy some inequalities conditions on metric spaces, J. Ineq. Appl. 343 (2015). [25] C. Suanoom and C. Klin-Eam, Remark on fundamentally non-expansive mappings in hyperbolic spaces, J. Nonlinear Sci. Appl. 9 (2016) 1952–1956. [26] C. Klin-Eam, C. Suanoom and S. Suantai, Dislocated quasi-b-metric spaces and fixed point theorems for cyclic weakly contractions, J. Nonlinear Sci. Appl. 9 (2016) 2779–2788. [27] C. Suanoom and C. Klin-Eam, Fixed point theorems for generalized nonexpansive mapping in hyperbolic spaces, J. Fixed Point Theory Appl. 19(4) (2017) 2511–2528. [28] C. Suanoom, C. Klin-Eam and W. Khuangsatung, Convergence theorems for a bivariate nonexpansive operator, Adv. Fixed Point Theory 8(3) (2018) 274–286. [29] C. Suanoom and W. Khuangsatung, Approximation of common solutions to proximal split feasibility problems and fixed point problems in Hilbert spaces, Thai J. Math. 16(4) (2018) 168–183. [30] C. Suanoom, K. Sriwichai, C. Klin-Eam and W. Khuangsatung, The generalized α-nonexpansive mappings and related convergence theorems in hyperbolic spaces, J. Inf. Math. Sci. 11(1) (2019) 1–17. [31] C. Suanoom, K. Sriwichai, C. Klin-Eam and W. Khuangsatung, The finite family L-Lipschitzian Suzuki generalized nonexpansive mappings, Comm. Math. Appl. 10(1) (2019) 55–69. [32] C. Suanoom, C. Chanmanee, and P. Muangkarn, Fixed point theorems for R00-Kanan mapping in b-metric spaces, 24th Ann. Meet. Math., 2019. [33] C. Suanoom, On ∆-convergence theorems in b-CAT(0) spaces, Thai J. Math., Special Issue: Ann. Meet. Math., 2019 (2020) 81–88 [34] W. Khuangsatung, S. Chan-iam, P.Muangkarn and C. Suanoom, The rectangular quasi-metric space and common fixed point theorem for ψ-contraction and ψ-Kannan mappings, Thai J. Math., Special Issue: Ann. Meet. Math. 2019, (2020) 89–101. [35] T. Bantaojai, C. Suanoom and W. Khuangsatung, The convergence theorem for a square α-nonexpansive mapping in a hyperbolic space, Thai J. Math. 18(3) (2021) 963–975. [36] C. Suanoom, T. Bantaojai, and W. Khuangsatung, Stability of a generalization of Cauchy’s and the quadratic functional equations in quasi-Banach spaces, Thai J. Math. 18(3) (2021) 1597–1609. | ||
آمار تعداد مشاهده مقاله: 15,465 تعداد دریافت فایل اصل مقاله: 659 |