Common Fixed Point Theorems on Compatibility and Continuity in Soft Metric Spaces
Keywords:Soft metric space, Soft element, Soft set, Soft mappings, Soft continuous mapping, Soft contractive mapping, Fixed point theorem
In this paper, basic notions of soft sets are introduced and some important properties of soft metric spaces are established. It is shown that soft metric extensions of several important fixed point theorems for metric spaces can be directly deduce from comparable existing results. Some examples are given to validate and illustrate the approach. Obtained results modify, improve, sharpen, enrich and generalize various known results.
M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Computers & Mathematics with Applications 57 (2009), 1547 – 1553, DOI: 10.1016/j.camwa.2008.11.009.
R. Bhardwaj, Q. A Kabir, R. Shrivastava and G. V. V. J. Rao, Common fixed point theorems using rational contraction in soft compact metric spaces, Turkish Journal of Computer and Mathematics Education 12(10) (2021), 2499 – 2503, DOI: 10.17762/turcomat.v12i10.4861.
R. Bhardwaj, S. A. Khaindait, S. Komal, V. Sharma, Q. A. Kabir and P. Konar, Results with cone metric spaces, Materials Today: Proceedings 47 (2021), 6987 – 6990, DOI: 10.1016/j.matpr.2021.05.277.
R. Bhardwaj, H. G. Sanath Kumar, B. K. Singh, Q. A. Kabir and P. Konar, Fixed point theorems in soft parametric metric space, Advances in Mathematics: Scientific Journal 9(12) (2020), 10189 – 10194, DOI: 10.37418/amsj.9.12.11.
D. Chen, E. C. C. Tsang, D. S. Yeung and X. Wang, The parameterization reduction of soft sets and its applications, Computers & Mathematics with Applications 49 (2005), 757 – 763, DOI: 10.1016/j.camwa.2004.10.036.
S. Das and S. K. Samanta, Soft real sets, soft real numbers and their properties, The Journal of Fuzzy Mathematics 20(3) (2012), 551 – 576.
S. Das and S. K. Samanta, Soft metric, Annals of Fuzzy Mathematics and Informatics 6(1) (2013), 77 – 94, URL: http://www.afmi.or.kr/papers/2013/Vol-06_No-01/AFMI-6-1(1--226)/AFMI-6-1(77--94)-J-120715R1.pdf.
S. Das and S. K. Samanta, On soft metric spaces, The Journal of Fuzzy Mathematics 21(3) (2013), 207 – 213.
˙I. Demir, O. B. Ozbakır and ˙I. Yıldız, On fixed soft element theorems in se-uniform spaces, Journal of Nonlinear Science and Applications 9 (2016), 1230 – 1242, DOI: 10.22436/jnsa.009.03.48.
C. Gunduz (Aras), A. Sonmez, H. Çakallı, On soft mappings, https://arxiv.org/abs/1305.4545v1 [math.GM], 16 May 2013.
M. Hakwadiya, R. K. Gujetiya and D. K. Mali, Fixed point theorem in complex valued metric spaces for continuityand compatibility, American International Journal of Research in Science, Technology, Engineering & Mathematics 7(3) (2014), 217 – 223, URL: http://iasir.net/AIJRSTEMpapers/AIJRSTEM14-588.pdf.
L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Application 332 (2007), 1468 – 1476, DOI: 10.1016/j.jmaa.2005.03.087.
S. Hussain and B. Ahmad, Some properties of soft topological spaces, Computers & Mathematics with Applications 62 (2011), 4058 – 4067, DOI: 10.1016/j.camwa.2011.09.051.
S. Kumar, H.G, R. Bhardwaj and B. K. Singh, Fixed point theorems of soft metric space using altering distance function, International Journal of Recent Technology and Engineering 7(6) (2019), 1804 – 1807, URL: https://www.ijrte.org/wp-content/uploads/papers/v7i6/F3150037619.pdf.
P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Computers & Mathematics with Applications 44 (2002), 1077 – 1083, DOI: 10.1016/S0898-1221(02)00216-X.
P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Computers & Mathematics with Applications 45 (2003), 555 – 562, DOI: 10.1016/S0898-1221(03)00016-6.
P. Majumdar and S. K. Samanta, On soft mappings, Computers & Mathematics with Applications 60 (2010), 2666 – 2672, DOI: 10.1016/j.camwa.2010.09.004.
D. Molodtsov, Soft set theory — First results, Computers & Mathematics with Applications 37 (1999), 19 – 31, DOI: 10.1016/S0898-1221(99)00056-5.
S. Raghuwanshi, V. Gupta, S. Ghosh, R. Bhardwaj and S. Rai, Fixed point theorems for complete metric spaces, Materials Today: Proceedings 47 (2021), 6996 – 6998, DOI: 10.1016/j.matpr.2021.05.279.
B. E. Rhoades, A comparison of various definition of contractive mappings, Transactions of the American Mathematical Society 226 (1977), 257 – 290, DOI: 10.1090/S0002-9947-1977-0433430-4.
B. Samet, C. Vetro and P. Vetro, Fixed point theorems for (alpha)-(psi)-contractive type mappings, Nonlinear Analysis: Theory, Methods and Applications 75(4) (2012), 2154 – 2165, DOI: 10.1016/j.na.2011.10.014.
M. Shabir and M. Naz, On soft topological spaces, Computers & Mathematics with Applications 61(2011), 1786 – 1799, DOI: 10.1016/j.camwa.2011.02.006.
I. Uddin, A. Perveen, H. Isık and R. Bhardwaj, A solution of Fredholm integral inclusions via Suzuki-type fuzzy contractions, Mathematical Problems in Engineering 2021 (2021), Article ID 6579405, 1 – 8, DOI: 10.1155/2021/6579405.
B. R. Wadkar, R. Bhardwaj and R. M. Sharraf, Couple fixed point theorems in soft metric spaces, Materials Today: Proceedings 29(2) (2020), 617 – 624, DOI: 10.1016/j.matpr.2020.07.323.
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