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On some fixed point theorems for multivalued F-contractions in partial metric spaces

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Języki publikacji
EN
Abstrakty
EN
Altun et al. explored the existence of fixed points for multivalued F-contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F-contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.
Wydawca
Rocznik
Strony
151--161
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
  • Department of Mathematics, P. O. Box: 35062 College of Natural and Applied Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania
  • Department of Mathematics, College of Natural and Mathematical Sciences, The University of Dodoma, Dodoma, Tanzania
Bibliografia
  • [1] D. O’Regan and A. Petruśel, Fixed point theorems for generalized contraction in ordered metric spaces, J. Math. Anal. Appl. 341(2008), no. 2, 1241-1252.
  • [2] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012(2012), 94.
  • [3] I. Altun, G. Minak, and H. Dag, Multivalued F-contractions on complete metric space, J. Nonlinear Convex Anal. 16(2015), no. 4, 659-666.
  • [4] M. Khamsi and W. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, John Wiley and Sons, Canada, 2001.
  • [5] M. Younis, D. Singh, and A. Petrusel, Applications of graph Kannan mappings to the damped spring-mass system and deformation of an elastic beam, Discrete Dyn. Nat. Soc. 2019(2019), 1315387, DOI: https://doi.org/10.1155/2019/1315387.
  • [6] M. Younis, D. Singh, and A. Goyal, A novel approach of graphical rectangular b-metric spaces with an application to the vibrations of a vertical heavy hanging cable, J. Fixed Point Theory Appl. 21(2019), 33, DOI: https://doi.org/10.1007/s11784-019-0673-3.
  • [7] M. Younis, D. Singh, M. Asadi, and V. Joshi, Results on contractions of Reich type in graphical b-metric spaces with applications, Filomat 33(2019), no. 17, 5723-5735, DOI: https://doi.org/10.2298/FIL1917723Y.
  • [8] S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30(1969), no. 2, 475-488.
  • [9] Ö. Acar, G. Durmaz, and G. Minak, Generalized multivalued F-contractions on complete metric spaces, Bulletin of the Iranian Mathematical Society 40(2014), no. 6, 1469-1478.
  • [10] S. Matthews, Partial metric topology in papers on general topology and applications, in: S. Andima et al. (eds.), Eighth Summer Conference at Queens College, Annals of the New York Academy of Sciences, 1992, vol. 728, pp. 183-197.
  • [11] D. Paesano and C. Vetro, Multi-valued F-contractions in 0-complete partial metric spaces with application to Volterra type integral equation, Rev. R. Acad. Cienc. Exactas, Fís. Nat. Madr. 108(2014), no. 2, 1005-1020.
  • [12] E. Karapinar, A. Fulga, and R. P. Agarwal, A survey: F-contractions with related fixed point results, J. Fixed Point Theory Appl. 22(2020), 69, DOI: https://doi.org/10.1007/s11784-020-00803-7.
  • [13] E. Karapinar, K. Taş, and V. Rakočević, Advances on fixed point results on partial metric spaces, in: K. Taş, D. Baleanu, J. Machado (eds.), Mathematical Methods in Engineering: Nonlinear Systems and Complexity, vol. 23, Springer, Cham, 2019, DOI: https://doi.org/10.1007/978-3-319-91065-9_1.
  • [14] M. Bukatin, R. Kopperman, and S. Matthews, Partial metric spaces, Amer. Math. Monthly 116(2009), no. 8, 708-718.
  • [15] M. Younisa, D. Singh, S. Radenovic, and M. Imdad, Convergence theorems for generalized contractions and applications, Filomat 34(2020), no. 3, 945-964.
  • [16] M. Younis, D. Singh, D. Gopal, A. Goyal, and M. S. Rathore, On applications of generalized F-contraction to differential equations, Nonlinear Funct. Anal. Appl. 24(2019), no. 1, 155-174.
  • [17] I. Altun and H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud. 1(2008), no. 1-2, 1-8.
  • [18] D. Pompeiu, Sur la continuit’e des fonctions de variables complexes (These), Gauthier-Villars, Paris, 1905; Ann. Fac. Sci. de Toulouse 7(1905), 264-315.
  • [19] F. Hausdorff, Grundzüge der Mengenlehre, Veit, Leipzig, (1914), ISBN 978-0-8284-0061-9, Reprinted by Chelsea Publishing Company in 1949.
  • [20] H. Aydi, M. Abbas, and C. Vetro, Partial Hausdorff metric and Nadleras fixed point theorem on partial metric spaces, Topology Appl. 159(2012), 3234-3242.
  • [21] A. Al-Rawashdeh, H. Aydi, A. Felhi, S. Sahmim, and W. Shatanawi, On common fixed points for α-F-contractions and applications, J. Nonlinear Sci. Appl. 9(2016), no. 5, 3445-3458.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
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