A use of pair (F; h) upper class on some fixed point results in probabilistic Menger space
DOI:
https://doi.org/10.5269/bspm.52878Resumen
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.
Referencias
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[5] K. Menger, Statistical metric, Proc. Natl. sci. 28, 535–538 (1942) .
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[8] V. M. Sehgal, T. A. Bharucha-Reid, Fixed point of contraction mappigs in PM-spaces, Math. Syst. Theory. 6, 97–102 (1972).
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[10] 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).
[11] M. Shams, Sh. Jafari, Some fixed point results in probabilistic Menger space, Bol. Soc. Paran. Mat. 35 (3) 9–24 (2017).
[12] Y. Liu, Zh. Li, Coincidence point theorems in probabilistic and fuzzy metric spaces, Fuzzy Sets Syst. 158, 58–70 (2007).
[13] D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets Syst. 144, 431–439 (2004).
[14] D. Mihet, Fixed point theorems in probabilistic metric spaces, Chaos Solitons Fractals 41, 1014–1019 (2009).
[15] J. Jachymski, On probabilistic Ï•-contractions on Menger spaces, Nonlinear Anal. 73, 2199–2203 (2010).
[16] 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).
[17] 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).
[18] 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).
[2] B. S. Choudhury, K. P. Das, A new contraction principle in Menger spaces, Acta Math. Sin. 24, 1379–1386 (2008) .
[3] 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).
[4] O. Hadzic, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer, Dordrecht (2001).
[5] K. Menger, Statistical metric, Proc. Natl. sci. 28, 535–538 (1942) .
[6] B. Schweizer, A. Sklar, Probabilistic Metric Space,Elsevier, North-Holland, New York (1983).
[7] J. Jachymski, On probabilistic Ï•-contractions on Menger spaces, Nonlinear Anal. 73, 2199–2203 (2010).
[8] V. M. Sehgal, T. A. Bharucha-Reid, Fixed point of contraction mappigs in PM-spaces, Math. Syst. Theory. 6, 97–102 (1972).
[9] 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).
[10] 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).
[11] M. Shams, Sh. Jafari, Some fixed point results in probabilistic Menger space, Bol. Soc. Paran. Mat. 35 (3) 9–24 (2017).
[12] Y. Liu, Zh. Li, Coincidence point theorems in probabilistic and fuzzy metric spaces, Fuzzy Sets Syst. 158, 58–70 (2007).
[13] D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets Syst. 144, 431–439 (2004).
[14] D. Mihet, Fixed point theorems in probabilistic metric spaces, Chaos Solitons Fractals 41, 1014–1019 (2009).
[15] J. Jachymski, On probabilistic Ï•-contractions on Menger spaces, Nonlinear Anal. 73, 2199–2203 (2010).
[16] 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).
[17] 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).
[18] 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).
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2022-12-26
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