Open Access

On existence of fixed points and applications to a boundary value problem and a matrix equation in C*−algebra valued partial metric spaces


Cite

[1] Hamed H Alsulami, Ravi P Agarwal, E. Karapınar and F. Khojasteh, A short note on C*−valued contraction mappings, J. Inequal. Appl., 2016(1) (2016), 1–3.10.1186/s13660-016-0992-5 Search in Google Scholar

[2] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux équation intégrales, Fund. Math., 3 (1922), 133–181.10.4064/fm-3-1-133-181 Search in Google Scholar

[3] S. Chandok, D. Kumar and C. Park, C∗−algebra valued partial metric space and fixed point theorems, J. Ind. Acad. Math., 129(3) (2019), 1–9.10.1007/s12044-019-0481-0 Search in Google Scholar

[4] S. K. Chatterjee, Fixed point theorem, C. R. Acad., Bulgar Sci., 25 (1972), 727–730. Search in Google Scholar

[5] J. Górnicki, Remarks on contractive type mappings, Fixed Point Theory Appl., 2017(1) (2016), 1–12.10.1186/s13663-017-0601-4 Search in Google Scholar

[6] G. E. Hardy and T. D. Roger, A generalization of a fixed point theorem of Reich, Cand. Math. Bull., 16(2), (1973), 201–206.10.4153/CMB-1973-036-0 Search in Google Scholar

[7] Z. Kadelburg and S. Radenovi, Fixed point results in C∗−algebra-valued metric spaces are direct consequences of their standard metric counterparts, Fixed Point Theory Appl., 2016(1) (2016), 1–6.10.1186/s13663-016-0544-1 Search in Google Scholar

[8] R. Kannan, Some results on fixed points-II, Amer. Math. Monthly, 76(4) (1969), 405–408.10.1080/00029890.1969.12000228 Search in Google Scholar

[9] Xiaoyan Lv and Yuqiang Feng, Some fixed point theorem for Reich type contraction in generalized metric spaces, J. Math. Anal. Appl., 9(5) (2018), 80–88. Search in Google Scholar

[10] Z. Ma, L. Jiang and H. Sun, C*−algebra-valued metric spaces and related fixed point theorems, Fixed Point Theory Appl., 206 (2014).10.1186/1687-1812-2014-206 Search in Google Scholar

[11] Z. Ma and L. Jiang, C*−Algebra-valued b−metric spaces and related fixed point theorems, Fixed Point Theory Appl., 222, (2015).10.1186/s13663-015-0471-6 Search in Google Scholar

[12] S. G. Matthews, Partial metric topology, General Topology and its Applications, Proc. 8th Summer Conf., Queens College, 1992. Ann. New York Acad. Sci., 728 (1994), 183–197.10.1111/j.1749-6632.1994.tb44144.x Search in Google Scholar

[13] G. J. Murphy, C*algebra and operator theory, Academic Press, London, (1990). Search in Google Scholar

[14] S. Reich, Some remarks concerning contraction mappings, Can. Math. Bull., 14, (1971), 121-124.10.4153/CMB-1971-024-9 Search in Google Scholar

[15] T. Senapati and L. Kanta Dey, Remarks on common fixed point results in C*-algebra-valued metric spaces, J. Inform. Math. Sci., 10(1 & 2) (2018), 333–337.10.26713/jims.v10i1-2.618 Search in Google Scholar

[16] A. Tomar, M. Joshi, and A. Deep, Fixed points and its applications in C*−algebra-valued partial metric space, TWMS J. App. and Eng. Math., 11(2) (2021), 329–340. Search in Google Scholar

[17] A. Tomar and M. Joshi, Note on results in C*−algebra-valued metric spaces, Electron. J. Math. Analysis Appl., 9(2) (2021), 262–264. https://doi.org/10.1007/s41478-019-00204-frac.org/Journals/EJMAA/ Search in Google Scholar

[18] Q. Xin, L. Jiang and Z. Ma, Common fixed point theorems in C*−algebra-valued metric spaces, J. Nonlinear Sci. Appl., 9(9) (2016), 4617–4627.10.22436/jnsa.009.06.100 Search in Google Scholar

[19] Q. H. Xu, T. E. D. Bieke, and Z. Q. Chen, Introduction to operator algebras and non commutative Lp−spaces, Science Press, Beijing, (2010) (In Chinese). Search in Google Scholar

eISSN:
2066-7752
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Mathematics, General Mathematics