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Some fixed point theorems in metric spaces by altering distances. (English) Zbl 1013.54011
Summary: A generalization is obtained for some of the fixed point theorems of M. S. Khan, M. Swaleh and S. Sessa [Bull. Aust. Math. Soc. 30, 1-9 (1984; Zbl 0553.54023)], H. K. Pathak and R. Sharma [Math. Educ. 28, No. 3, 151-157 (1994; Zbl 0907.54041)], and K. P. R. Sastry and G. V. R. Babu for a self-map on a metric space, which involve the idea of alteration of distances between points.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
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References:
[1] M. S. Khan, M. Swaleh and S. Sessa: Fixed point theorems by altering distances between the points. Bull. Austral. Math. Soc. 30 (1984), 1-9. · Zbl 0553.54023
[2] S. V. R. Naidu: Fixed point theorems by altering distances. Adv. Math. Sci. Appl. 11 (2001), 1-16. · Zbl 1001.54029
[3] H. K. Pathak and Rekha Sharma: A note on fixed point theorems of Khan, Swaleh and Sessa. Math. Edn. 28 (1994), 151-157. · Zbl 0907.54041
[4] B. E. Rhoades: A comparison of various definitions of contractive mappings. Trans. Amer. Math. Soc. 226 (1977), 257-290. · Zbl 0365.54023
[5] K. P. R. Sastry and G. V. R. Babu: Fixed point theorems in metric spaces by altering distances. Bull. Calcutta Math. Soc. 90 (1998), 175-182. · Zbl 0953.54040
[6] K. P. R. Sastry and G. V. R. Babu: Some fixed point theorems by altering distances between the points. Indian J. Pure Appl. Math. 30 (1999), 641-647. · Zbl 0938.47044
[7] K. P. R. Sastry and G. V. R. Babu: Some fixed point theorems in complete metric spaces by altering distances. Preprint. · Zbl 1002.54028
[8] K. P. R. Sastry and S. V. R. Naidu: Fixed point theorems for generalised contraction mappings. Yokohama Math. J. 28 (1980), 15-29. · Zbl 0464.54047
[9] M. R. Tasković: Some new principles in fixed point theory. Math. Japon. 35 (1990), 645-666. · Zbl 0709.47048
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