Geodesic
Caristi's fixed point theorem in probabilistic metric spaces
Kybernetika, Tome 57 (2021) no. 1, pp. 46-59
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In this work, we define a partial order on probabilistic metric spaces and establish some new Caristi's fixed point theorems and Ekeland's variational principle for the class of (right) continuous and Archimedean t-norms. As an application, a partial answer to Kirk's problem in metric spaces is given.
In this work, we define a partial order on probabilistic metric spaces and establish some new Caristi's fixed point theorems and Ekeland's variational principle for the class of (right) continuous and Archimedean t-norms. As an application, a partial answer to Kirk's problem in metric spaces is given.
DOI : 10.14736/kyb-2021-1-0046
Classification : 47H10, 58E30
Keywords: probabilistic metric space; Caristi's fixed point; Archimedean t-norm 
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Fathi Vajargah, Kianoush; Mottaghi Golshan, Hamid; Arjomand Far, Abbas. Caristi's fixed point theorem in probabilistic metric spaces. Kybernetika, Tome 57 (2021) no. 1, pp. 46-59. doi: 10.14736/kyb-2021-1-0046

[1] Abbasi, N., Golshan, H. Mottaghi: Caristi's fixed point theorem and its equivalences in fuzzy metric spaces. Kybernetika 52 (2016), 6, 966-979. | MR

[2] Amini-Harandi, A.: Some generalizations of Caristi's fixed point theorem with applications to the fixed point theory of weakly contractive set-valued maps and the minimization problem. Nonlinear Anal. 72 (2010), 12, 4661-4665. | DOI | MR

[3] Boyd, D. W., Wong, J. S. W.: On nonlinear contractions. Proc. Amer. Math. Soc. 20 (1969), 458-464. | DOI | MR

[4] Caristi, J.: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Amer. Math. Soc. 215 (1976), 241-251. | DOI | MR | Zbl

[5] Caristi, J., Kirk, W. A.: Geometric fixed point theory and inwardness conditions. In: The geometry of metric and linear spaces (Proc. Conf., Michigan State Univ., East Lansing, Mich., 1974), pp. 74-83. Lecture Notes in Math., Vol. 490. Springer, Berlin 1975. | DOI | MR | Zbl

[6] Chang, S.-S., Cho, Y. J., Kang, S.-M.: Nonlinear Operator Theory in Probablistic Metric Spaces. Nova Publishers, 2001. | MR

[7] George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets and Systems 64 (1994), 3, 395-399. | DOI | MR | Zbl

[8] Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems 27 (1988), 3, 385-389. | DOI | MR | Zbl

[9] Gregori, V., Miñana, J.-J., Morillas, S.: Some questions in fuzzy metric spaces. Fuzzy Sets and Systems 204 (2012), 71-85. | DOI | MR | Zbl

[10] Gregori, V., Morillas, S., Sapena, A.: On a class of completable fuzzy metric spaces. Fuzzy Sets and Systems 161 (2010), 16, 2193-2205. | DOI | MR | Zbl

[11] Hadzic, O., Pap, E.: Fixed Point Theory in Probabilistic Metric Spaces. Springer Science and Business Media, 2013. | MR

[12] Jachymski, J. R.: Caristi's fixed point theorem and selections of set-valued contractions. J. Math. Anal. Appl. 227 (1998), 1, 55-67. | DOI | MR

[13] Khamsi, M. A.: Remarks on Caristi's fixed point theorem. Nonlinear Anal. 71 (2009), 1-2, 227-231. | DOI | MR

[14] Khamsi, M. A., Kirk, W. A.: An Introduction to Metric Spaces and Fixed Point Theory. John Wiley and Sons, 2011. | MR

[15] Khamsi, M. A., Misane, D.: Compactness of convexity structures in metrics paces. Math. Japon. 41 (1995), 321-326. | MR

[16] Klement, E., Mesiar, R.: Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms. Elsevier Science, 2005. | MR

[17] Klement, E. P., Mesiar, R., Pap, E.: A characterization of the ordering of continuous t-norms. Fuzzy Sets and Systems 86 (1997), 2, 189-195. | DOI | MR

[18] Klement, E. P., Mesiar, R., Pap, E.: Triangular norms. Trends in Logic-Studia Logica Library 8, Kluwer Academic Publishers, Dordrecht 2000. | MR | Zbl

[19] Klement, E. P., Mesiar, R., Pap, E.: Triangular norms. position paper ii: general constructions and parameterized families. Fuzzy Sets and Systems 145 (2004), 3, 411-438. | DOI | MR

[20] Klement, E. P., Mesiar, R., Pap, E.: Triangular norms. position paper iii: continuous t-norms. Fuzzy Sets and Systems 145 (2004), 3, 439-454. | DOI | MR

[21] Kolesárová, A.: A note on archimedean triangular norms. BUSEFAL 80 (1999), 57-60.

[22] Kramosil, I., Michálek, J.: Fuzzy metrics and statistical metric spaces. Kybernetika 11 (1075), 5, 336-344. | MR | Zbl

[23] Menger, K.: Statistical metrics. Proc. Nat. Acad. Sci. U. S. A. 28 (1942), 535-537. | DOI | MR | Zbl

[24] Moore, J. C.: Mathematical Methods for Economic Theory 1. Springer Science and Business Media, 1999. | MR

[25] Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific J. Math. 10 (1960), 313-334. | DOI | MR | Zbl

[26] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing Co., New York 1983. | MR | Zbl

[27] Sedghi, S., Shobkolaei, N., Altun, I.: A new approach to Caristi's fixed point theorem on non-Archimedean fuzzy metric spaces. Iran. J. Fuzzy Syst. 12 (2015), 2, 137-143, 157. | MR

[28] Zeidler, E.: Nonlinear functional analysis and its applications I (Fixed-point theorems). Springer-Verlag, New York 1986. | DOI | MR

[29] Zermelo, E.: Neuer Beweis für die Möglichkeit einer Wohlordnung. Math. Ann. 65 (1907), 1, 107-128. | DOI | MR

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