Abstract
The main result of this paper is a fixed point theorem of self-mappings in Menger spaces which satisfy certain inequality. This inequality involves a class of real functions which we call Φ-functions. As a corollary we obtain a result in the corresponding metric spaces. The result is supported by an example. The class of real functions we have used is the conceptual extension of altering distance functions used in metric fixed point theory.
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G. V. R. Babu, B. Latitha and M. L. Sandhya, Common fixed point theorem involving two generalized altering distance functions in four variables, Proc. Jangjeon Math. Soc., 10 (2007), 83–93.
S. S. Chang, B. S. Lee, Y. J. Cho, Y. Q. Chen, S. M. Kang and J. S. Jung, Generalised contraction mapping principle and differential equation in probabilistic metric spaces, Proc. Amer. Math. Soc., 124 (1996), 2367–2376.
B. S. Choudhury and P. N. Dutta, A unified fixed point result in metric spaces involving a two variable function, FILOMAT, 14 (2000), 43–48.
B. S. Choudhury, A unique common fixed point theorem for a sequence of self mappings in Menger spaces, Bull. Kor. Math. Soc., 37 (2000), 569–575.
B. S. Choudhury, A common unique fixed point result in metric spaces involving generalized altering distances, Mathematical Communications, 10 (2005), 105–110.
B. S. Choudhury and P. N. Dutta, Common fixed points for fuzzy mappings using generalized altering distances, Soochow J. Math., 31 (2005), 71–81.
B. S. Choudhury and K. P. Das, A new contraction principle in Menger spaces, Acta Mathematica Sinica, English series, 24 (2008), 1379–1386.
I. Golet, On contractions in probabilistic spaces, Radovi Matematicki, 13 (2004), 87–92.
O. Hadzic and E. Pap, Fixed Point Theory In Probabilistic Metric Spaces, Kluwer Academic Publishers (2001).
O. Hadzic, E. Pap and V. Radu, Generalized contraction mapping principle in probabilistic metric space, Ada Math. Hungar., 101 (2003), 131–148.
M. Imdad and L. Khan, Common fixed point theorems for nonself-mappings in metrically convex spaces via altering distances, Int. J. Math. Math. Sci., 24 (2005), 4029–4039.
M. S. Khan, M. Swaleh and S. Sessa, Fixed points theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1–9.
J. K. Kholi and S. Vashistha, Common fixed point theorems in probabilistic metric spaces, Acta Math. Hungar., 115 (2007), 37–47.
D. Mihet, On the existence and the uniqueness of fixed points of Sehgal contractions, Fuzzy Sets and Systems, 156 (2005), 135–141.
D. Mihet, A generalization of contraction principle in probabilistic metric spaces. Part - II, Int. J. Math. Math. Sci., 5 (2005), 729–736.
S. V. R. Naidu, Some fixed point theorems in metric spaces by altering distances, Czechoslovak Math. J., 53(128) (2003), 205–212.
K. P. R. Sastry and G. V. R. Babu, Fixed point theorems in metric space by altering distances, Bull. Cal. Math. Soc., 90 (1998), 175–185.
K. P. R. Sastry and G. V. R. Babu, Some fixed point theorems by altering distances between the points, Ind. J. Pure. Appl. Math., 30 (1999), 641–647.
K. P. R. Sastry, S. V. R. Naidu, G. V. R. Babu and G. A. Naidu, Generalization of fixed point theorems for weekly commuting maps by altering distances, Tamkang J. Math., 31 (2000), 243–250.
B. Schweizer and A. Sklar, Probabilistic Metric Space, North-Holland (Amsterdam, 1983).
V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric space, Math. Sys. Theory, 6 (1972), 97–100.
B. Singh and S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl., 301 (2005), 439–448.
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Choudhury, B.S., Das, K. & Dutta, P.N. A fixed point result in Menger spaces using a real function. Acta Math Hung 122, 203–216 (2009). https://doi.org/10.1007/s10474-008-7242-3
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DOI: https://doi.org/10.1007/s10474-008-7242-3