A use of pair (F; h) upper class on some fixed point results in probabilistic Menger space
Resumo
In this paper, we define the concept of (F; h)-alpha-beta-contractive mappings in probabilistic Menger space and prove some fixed point theorems for such mappings. Some examples are given to support the obtained results.
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Referências
N. A. Babacev, Nonlinear generalized contraction on Menger PM-spaces, Appl. Anal. Discrete Math. 6, 257–264 (2012). DOI: https://doi.org/10.2298/AADM120526012B
B. S. Choudhury, K. P. Das, A new contraction principle in Menger spaces, Acta Math. Sin. 24, 1379–1386 (2008) . DOI: https://doi.org/10.1007/s10114-007-6509-x
D. Gopal, M. Abbas, C. Vetro,Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation, Appl Math and Comput. 232 , 955–967 (2014). DOI: https://doi.org/10.1016/j.amc.2014.01.135
O. Hadzic, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer, Dordrecht (2001). DOI: https://doi.org/10.1007/978-94-017-1560-7
K. Menger, Statistical metric, Proc. Natl. sci. 28, 535–538 (1942) . DOI: https://doi.org/10.1073/pnas.28.12.535
B. Schweizer, A. Sklar, Probabilistic Metric Space,Elsevier, North-Holland, New York (1983).
J. Jachymski, On probabilistic ϕ-contractions on Menger spaces, Nonlinear Anal. 73, 2199–2203 (2010).
V. M. Sehgal, T. A. Bharucha-Reid, Fixed point of contraction mappigs in PM-spaces, Math. Syst. Theory. 6, 97–102 (1972). DOI: https://doi.org/10.1007/BF01706080
A. H. Ansari, Note on α-admissible mappings and related fixed point theorems , The 2nd Regional Conference on Mathematics And Applications, PNU, 373–376 (2014).
A. H. Ansari and S. Shukla, Some fixed point theorems for ordered F-(F, h)-contraction and subcontractions in 0-forbitally complete partial metric spaces, J. Adv. Math. Stud. 9(1), 37–53 (2016).
M. Shams, Sh. Jafari, Some fixed point results in probabilistic Menger space, Bol. Soc. Paran. Mat. 35 (3) 9–24 (2017). DOI: https://doi.org/10.5269/bspm.v35i3.29791
Y. Liu, Zh. Li, Coincidence point theorems in probabilistic and fuzzy metric spaces, Fuzzy Sets Syst. 158, 58–70 (2007). DOI: https://doi.org/10.1016/j.fss.2006.07.010
D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets Syst. 144, 431–439 (2004). DOI: https://doi.org/10.1016/S0165-0114(03)00305-1
D. Mihet, Fixed point theorems in probabilistic metric spaces, Chaos Solitons Fractals 41, 1014–1019 (2009). DOI: https://doi.org/10.1016/j.chaos.2008.04.030
J. Jachymski, On probabilistic ϕ-contractions on Menger spaces, Nonlinear Anal. 73, 2199–2203 (2010). DOI: https://doi.org/10.1016/j.na.2010.05.046
T. Dosenovic, P. Kumam, D. Gopal, D. K. Patel, and A. Takaci, On fixed point theorems involving altering distances in Menger probabilistic metric spaces, J Inequal Appl 1, 1–10 (2013). DOI: https://doi.org/10.1186/1029-242X-2013-576
M. Hasanuzzaman, and M. Imdad, Relation theoretic metrical fixed point results for Suzuki type ZR-contraction with an application, AIMS Mathematics, 5(3), 2071–2087 (2020). DOI: https://doi.org/10.3934/math.2020137
N. Wairojjana, T. Dosenovic, D. Rakic, D. Gopal, and P. Kumam, An altering distance function in fuzzy metric fixed point theorems, Fixed Point Theory A, 1, 1–19 (2015). DOI: https://doi.org/10.1186/s13663-015-0318-1
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