Research article

Common fixed point on the $b_v(s)$-metric space of function-valued mappings

  • Received: 22 July 2020 Accepted: 04 November 2020 Published: 09 November 2020
  • MSC : 47H10, 54H25

  • In this paper, some common fixed point results are obtained in $b_v(s)$-metric spaces. $b_v(s)$-metric space generalizes not only $b$-metric space but also rectangular metric space, $v$-generalized metric space and rectangular $b$-metric space. Examples show how these results can be applied in concrete situations.

    Citation: Tayebe Lal Shateri, Ozgur Ege, Manuel de la Sen. Common fixed point on the $b_v(s)$-metric space of function-valued mappings[J]. AIMS Mathematics, 2021, 6(2): 1065-1074. doi: 10.3934/math.2021063

    Related Papers:

  • In this paper, some common fixed point results are obtained in $b_v(s)$-metric spaces. $b_v(s)$-metric space generalizes not only $b$-metric space but also rectangular metric space, $v$-generalized metric space and rectangular $b$-metric space. Examples show how these results can be applied in concrete situations.


    加载中


    [1] M. S. Abdullahi, P. Kumam, Partial bv(s)-metric spaces and fixed point theorems, J. Fixed Point Theory Appl., 20 (2018), 1-13. doi: 10.1007/s11784-018-0489-6
    [2] S. Aleksic, Z. D. Mitrovic, S. Radenovic, A fixed point theorem of Jungck in bv(s)-metric spaces, Period. Math. Hung., 77 (2018), 224-231. doi: 10.1007/s10998-018-0236-1
    [3] A. Amini-Harandi, Fixed point theory for quasi-contraction maps in b-metric spaces, Fixed Point Theory, 15 (2014), 351-358.
    [4] T. V. An, L. Q. Tuyen, N. V. Dung, Stone-type theorem on b-metric spaces and applications, Topol. Appl., 185 (2015), 50-64.
    [5] H. Aydi, M. F. Bota, E. Karapinar, S. Mitrović, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory Appl., 2012 (2012), 88.
    [6] H. Aydi, D. Bajovic, Z. D. Mitrovic, Some common fixed point results in partial bv(s)-metric spaces, Acta Math. Univ. Comenianae, 89 (2019), 153-160.
    [7] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst., 30 (1989), 26-37.
    [8] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11.
    [9] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Math. Fis. Univ. Modena, 46 (1998), 263-276.
    [10] P. Dhawana, J. Kaura, V. Gupta, Novel results on a fixed function and their application based on the best approximation of the treatment plan for tumour patients getting intensity modulated radiation therapy (IMRT), Proc. Est. Acad. Sci., 68 (2019), 223-234. doi: 10.3176/proc.2019.3.01
    [11] F. Dong, P. Ji, X. Wang, Pata-type fixed point results in bv(s)-metric spaces, Int. J. Anal. Appl., 17 (2019), 342-360.
    [12] D. Dukić, Z. Kadelburg, S. Radenović, Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstract Appl. Anal., 2011 (2011), 1-13.
    [13] O. Ege, Complex valued rectangular b-metric spaces and an application to linear equations, J. Nonlinear Sci. Appl., 8 (2015), 1014-1021. doi: 10.22436/jnsa.008.06.12
    [14] Y. U. Gaba, O. S. Iyiola, Advances in the study of metric type spaces, Appl. Math. Sci., 9 (2015), 4179-4190.
    [15] Y. U. Gaba, Metric type spaces and λ-sequences, Quaest. Math., 40 (2017), 49-55. doi: 10.2989/16073606.2016.1260068
    [16] R. George, C. Alaca, K. P. Reshma, On best proximity points in b-metric space, J. Nonlinear Anal. Appl., 2015 (2015), 45-56.
    [17] M. Geraghty, On contractive mappings, Proc. Am. Math. Soc., 40 (1973), 604-608.
    [18] N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic weakly (ψ, φ, L, A, B)-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 256 (2013), 1-18.
    [19] M. Iqbal, A. Batool, O. Ege, M. de la Sen, Fixed point of almost contraction in b-metric spaces, J. Math., 2020 (2020), 1-6.
    [20] O. S. Iyiola, Y. U. Gaba, On metric type spaces and fixed point theorems, Appl. Math. Sci., 8 (2014), 3905-3920.
    [21] I. Karahan, I. Isik, Generalizations of Banach, Kannan and Ciric fixed point theorems in bv(s)-metric spaces, U.P.B. Sci. Bull., Series A, 81 (2019), 73-80.
    [22] M. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., 2010 (2010), 315398. doi: 10.1155/2010/315398
    [23] M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129. doi: 10.1016/j.na.2010.06.084
    [24] Z. D. Mitrovic, S. Radenovic, The Banach and Reich contractions in bv(s)-metric spaces, J. Fixed Point Theory Appl., 19 (2017), 3087-3095. doi: 10.1007/s11784-017-0469-2
    [25] Z. D. Mitrovic, H. Aydi, Z. Kadelburg, G. S. Rad, On some rational contractions in bv(s)-metric spaces, Rend. Circ. Mat. Palermo (2), 69 (2020), 1193-1203. doi: 10.1007/s12215-019-00465-6
    [26] Z. D. Mitrovic, S. Radenovic, On Meir-Keeler contraction in Branciari b-metric spaces, Trans. A. Razmadze Math. Inst., 173 (2019), 83-90.
    [27] Z. D. Mitrovic, H. Aydi, S. Radenovic, On Banach and Kannan type results in cone bv(s)-metric spaces over Banach algebra, Acta Math. Univ. Comenianae, 89 (2020), 143-152.
    [28] Z. D. Mitrovic, L. K. Dey, S. Radenovic, A fixed point theorem of Sehgal-Guseman in bv(s)-metric spaces, An. Univ. Craiova, Math. Comput. Sci. Ser., in press (2020), 1-7.
    [29] H. K. Nashine, Z. Kadelburg, Cyclic generalized $\varphi$-contractions in b-metric spaces and an application to integral equations, Filomat, 28 (2014), 2047-2057. doi: 10.2298/FIL1410047N
    [30] J. R. Roshan, V. Parvaneh, Z. Kadelburg, N. Hussain, New fixed point results in b-rectangular metric spaces, Nonlinear Anal. Model. Control, 21 (2016), 614-634. doi: 10.15388/NA.2016.5.4
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3574) PDF downloads(297) Cited by(1)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog