Abstract
In this paper, we consider, discuss, and update some recent results on simulation functions established by several authors. By using one lemma of Radenović et al. (Bull. Iran. Math. Soc., 2012, 38 (3), 625–645), we suggest much shorter and nicer proofs of some statements than the ones available in the literature.
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References
F. Khojasteh, S. Shukla, and S. Radenovic, “A new approach to the study of fixed point theory for simulation functions,” Filomat 29, 1189–1194 (2015). doi 10.2298/FIL1506189K
H. Argoubi, B. Samet, and C. Vetro, “Nonlinear contractions involving simulation functions in a metric space with a partial order,” J. Nonlinear Sci. Appl. 8, 1082–1094 (2015).
A. Nastasi and P. Vetro, “Fixed point results on metric and partial metric spaces via simulation functions,” J. Nonlinear Sci. Appl. 8, 1059–1069 (2015).
A.-F. Roldán-López-de-Hierro, E. Karapinar, C. Roldán-López-de-Hierro, and J. Martínez-Moreno, “Coincidence point theorems on metric spaces via simulation functions,” J. Comput. Appl. Math. 275, 345–355 (2015). doi 10.1016/j.cam.2014.07.011
M. Demma, R. Saadati, and P. Vetro, “Fixed point results on b-metric space via Picard sequences and b-simulation functions,” Iran. J. Math. Sci. Inf. 11, 123–136 (2016). doi 10.7508/ijmsi.2016.01.011
E. Karapinar, “Fixed points results via simulation functions,” Filomat 30, 2343–2350 (2016). doi 10.2298/FIL1608343K
A. Nastasi and P. Vetro, “Existence and uniqueness for a first-order periodic differential problem via fixed point results,” Results Math. 71, 889–909 (2017). doi 10.1007/s00025-016-0551-x
F. Tchier, C. Vetro, and F. Vetro, “Best approximation and variational inequality problems involving a simulation function,” Fixed Point Theory Appl. 26 (2016). doi 10.1186/s13663-016-0512-9
S. Radenovic, Z. Kadelburg, D. Jandrlic, and A. Jandrlic, “Some results on weakly contractive maps,” Bull. Iran. Math. Soc. 38, 625–645 (2012).
S. Radenovic, “A note on tripled coincidence and tripled common fixed point theorems in partially ordered metric spaces,” Appl. Math. Comput. 236, 367–372 (2014). doi 10.1016/j.amc.2014.03.059
S. Radenovic, “Coupled fixed point theorems for monotone mappings in partially ordered metric spaces,” Krag. J. Math. 38, 249–257 (2014).
S. Radenovic, “Remarks on some coupled coincidence point results in partially ordered metric spaces,” Arab J. Math. Sci. 20, 29–39 (2014). doi 10.1016/j.ajmsc.2013.02.003
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Original Russian Text © D. Dolićanin-Đekić, 2017, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2017, Vol. 62, No. 4, pp. 579–585.
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Dolićanin-Đekić, D. Some new results on simulation functions. Vestnik St.Petersb. Univ.Math. 50, 349–353 (2017). https://doi.org/10.3103/S1063454117040069
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DOI: https://doi.org/10.3103/S1063454117040069