Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics
how to cite this article
share this article


  • citations in SCIndeks: 0
  • citations in CrossRef:[2]
  • citations in Google Scholar:[]
  • visits in previous 30 days:25
  • full-text downloads in 30 days:23


article: 1 from 6  
Back back to result list
Generalized 2-proximal C-contraction mappings in complete ordered 2-metric space and their best proximity points
aQuchan University of Technology, Quchan, Iran
bShahrood University of Technology, Shahrood, Iran
cVellore Institute of Technology (VIT) University, School of Advanced Sciences, Vellore, India
dIndira Gandhi National Tribal University, Amarkantak, Madhya Pradesh, India
Keywords: 2-proximal C-contraction mapping; best proximity point; 2-metric space
In this paper, we extend the concept of best proximity point to 2-metric spaces and prove the existence of such points for contraction type non-self mappings in the setting of complete 2-metric spaces. Also, we presented an example to support our results.
Aliouche, A., Simpson, C. (2012) Fixed points and lines in 2-metric spaces. Advances in Mathematics, 229(1): 668-690
An, V.T., Dung, V.N., Hang, V.T.L. (2014) General fixed point theorems on metric spaces and 2-metric spaces. Filomat, 28(10): 2037-2045
Basha, S. S. (2012) Best proximity point theorems on partially ordered sets. Optim. Lett
Ciric, L. (2003) Some recent results in metrical fixed point theory. Beograd: University of Belgrade
Deepmala (2014) A study on fixed point theorems for nonlinear contractions and its applications. Raipur, Chhatisgarh, India: Pt. Ravishankar Shukla University, Ph.D. Thesis
Dey, D., Saha, M. (2013) Some common fixed point theorems in a complete 2-metric space. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math, 52(1): 79-87
Dung, N.V., Hieu, N.T., Ly, N.T.T., Thinh, V.D. (2013) Remarks on the fixed point problem of 2-metric spaces. Fixed Point Theory and Applications, 2013(1): 167-167
Dung, N.V., Le, H.V.T. (2013) Fixed point theorems for weakly C-contractive mappings in ordered 2-metric spaces. Fixed Point Theory Appl, 161 (2013), 1-14
Freese, R.W., Cho, Y.J. (2001) Geometry of linear 2-normed space. Hauppauge, NY, USA: Nova Science Publishers
Gahler, V. S. (1963/1964) 2-metrische Räume und ihre topologische Struktur. Mathematische Nachrichten, 26(1-4): 115-148
Gupta, V., Kaur, R. (2012) Some common fixed point theorems for a class of A-contractions on 2-metric space. Int. J. Pure Appl. Math, 78(6): 909-916
Harjani, J., López, B., Sadarangani, K. (2011) Fixed point theorems for weakly C-contractive mappings in ordered metric spaces. Computers & Mathematics with Applications, 61(4): 790-796
Iseki, K. (1975) Fixed point theorems in 2-metric spaces. Math. Seminar Notes, Kobe Univ, 3, pp. 133-136
Kiran, Q., Ali, M.U., Kamran, T., Karapınar, E. (2015) Existence of best proximity points for controlled proximal contraction. Fixed Point Theory and Applications, 2015(1): 207-213
Kirk, W., Shahzad, N. (2014) Fixed point theory in distance spaces. Switzerland: Springer International Publishing
Latif, A. (2012) A fixed point result for multivalued generalized contraction maps. Filomat, vol. 26, br. 5, str. 929-933
Liu, X., Zhou, M., Mishra, L.N., Mishra, V.N., Damjanović, B. (2018) Common fixed point theorem of six self-mappings in Menger spaces using (CLRST) property. Open Mathematics, 16(1): 1423-1434
Mishra, L.N., Tiwari, S.K., Mishra, V.N. (2015) Fixed point theorems for generalized weakly S-contractive mappings in partial metric spaces. Journal of Applied Analysis and Computation, 5(4): 600-612
Mishra, L.N., Tiwari, S.K., Mishra, V.N., Khan, I.A. (2015) Unique fixed point theorems for generalized contractive mappings in partial metric spaces. Journal of Function Spaces, 2015: 1-8, article ID 960827, 8 pages
Mongkolkeha, C., Cho, Y.J., Kumam, P. (2013) Best proximity points for generalized proximal C-contraction mappings in metric spaces with partial orders. Journal of Inequalities and Applications, 2013(1): 94-105
Naidu, S.V.R., Prasad, J. R. (1986) Fixed points theorems in 2-metric spaces. Indian J. Pure Appl. Math, 17 (8): 974-993
Pathak, H.K., Deepmala (2013) Common fixed point theorems for PD-operator pairs under relaxed conditions with applications. Journal of Computational and Applied Mathematics, 239: 103-113
Reich, S. (1978) Approximate selections, best approximations, fixed points, and invariant sets. Journal of Mathematical Analysis and Applications, 62(1): 104-113
Rhoades, B.E. (2007) A biased discussion of fixed point theory. Carpathian J. Math, 23(1-2): 11-26
Saha, M., Dey, D. (2010) Fixed point theorems for a class of A-contractions on a 2-metric space. Novi Sad Journal of Mathematics, vol. 40, br. 1, str. 3-8
Singh, S.L. (1979) Some contractive type principles on 2-metric spaces and applications. Math. Sem. Notes Kobe Univ, 7(1): 1-11
Todorcevic, V. (2019) Harmonic quasiconformal mappings and hiperbolic type metrics. Springer Nature Switzerland AG
White, A. (1969) 2-Banach spaces. Mathematische Nachrichten, 42(1-3): 43-60


article language: English
document type: unclassified
DOI: 10.5937/SPSUNP2001001S
received: 29/11/2019
accepted: 03/03/2020
published in SCIndeks: 26/02/2021

Related records