Fixed Point Theorems Under Caristi’s Type Map on C∗ -Algebra Valued Fuzzy Soft Metric Space
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Keywords:
Bounded below function, Caristi’s mapping, C∗-algebra-valued Fuzzy soft metric, completeness, fixed point, Lower semi continuity.Abstract
In this paper, we present the extension of Caristi’s fixed point theorems for mappings defined on C∗-algebra-valued Fuzzy soft metric spaces. We establish the existence of simple proof of caristi’s type fixed point theorems in C∗-algebra-valued Fuzzy soft metric spaces and we give some examples which supports our main results.
References
Maji, Pk., Biswas, R and Roy, A. R., “Fuzzy soft Sets". Journal of
Fuzzy Mathematics, Vol9, no3 (2001) 589-602.
Thangaraj Beaula and Christinal Gunaseeli., on fuzzy soft
metric spaces. Malaya J. Mat.2 (3) (2015), 438-442.
Molodstov. D. A; “Fuzzy soft Sets"- First Result, Computers
View more references (27)
and Mathematics with Application, Vol.37 (1999) 19-31.
Roy, S. and Samanta T. K., “A note on Fuzzy soft Topological
Spaces", Annals of Fuzzy Mathematics and Informatics .2011.
Tanay, B, and Kandemir, M. B.,”Topological Structure of fuzzy
soft sets", Comput. Math. Appl. 61(2011), 2952-2957.
Thangaraj Beaula, R.Raja., Completeness in Fuzzy Soft Metric
Space. Malaya J. Mat. S (2) (2014), 197-20220(1), (2015), 55-67.
Caristi, J., Fixed point theorems for mappings satisfying inwardness conditions. Trans. Amer. Math. Soc., 215 (1976), 241-251. http://dx.doi.org/10.1090/s0002-9947-1976-0394329-4.
S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations integrales”, Fund. Math, 3 , 1922, 133-181.1.
Agarwal, RP, Khamsi, MA; Extension of Caristis´ fixed point
theorem to vector valued metric space. Nonlinear Anal. TMA
, 141-145(2011), doi: 10. 1016/j.na. 2010.08.025.
Dur-e-Shehwar,et.al., Caristis´ fixed point theorem on C∗-algebra valued metric spaces. J. Nonlinear Sci. Appl.9 (2016), 584-588.
Ekeland, I., On the variational principal. J. Math. Anal. Appl.
(2), 324-353 (1974).
Erdal Karapinar., Generalization of Caristi Kirks´ Theorem on partial metric spaces. Fixed point theory and Applications 2011, 2011:4.
Farshid Khojasteh, et. al., some applications of Caristis´ fixed
point theorem in metric spaces. Fixed point theory and Applications (2016), 2016:16.
M. A. Khamsi, W. A. Kirk, An Introduction to metric spaces
and fixed point theory, Wiley-Inter science, New York, (2001), http://dx.doi.org/10.1002/9781118033074.
M. A. Khamsi., Remarks on Caristis´ fixed point theorem. Nonlinear Anal, 71 (2009), 227-231. 1.
Wei-Shih Du., A Direct Proof of Caristis Fixed Point Theorem.
Applied Mathematical Sciences, Vol. 10, 2016, no. 46, 2289 -
Ma, ZH, Jiang, LN, Sun, HK. C∗ -algebra valued metric space
and related fixed point theorems. Fixed point theory Appl.2014.
ID 206(2014), 11 pages. 1, 2, 2.5, 3.6.
G.J. Murphy., C∗ -algebras and Operator Theory. Academic press, Boston (1990).2.