Graphical cyclic $\mathcal{J}$-integral Banach type mappings and the existence of their best proximity points
محورهای موضوعی : Operator theory
1 - Department of Mathematics, Payame Noor University, Tehran, Iran
2 - Department of Mathematics, Payame Noor University, Tehran, Iran
کلید واژه: graphical metric spaces, best proximity point, $\mathcal{J}$-quasi-contraction, orbitally $\mathcal{J}$-continuous,
چکیده مقاله :
The underlying aim of this paper is first to state the cyclicversion of $\mathcal{J}$-integral Banach type contractive mappings introduced by Fallahi, Ghahramani and Soleimani Rad[Integral type contractions in partially ordered metric spaces and best proximity point, Iran. J. Sci. Technol. Trans. Sci. 44 (2020), 177-183] and second to show the existence of best proximity points for such contractive mappings in a metric space with a graph, which can entail a large number of former best proximity point results. One fundamental issue that can be distinguished between this work and previous researches is that it can also involve all of results stated by taking comparable and $\vartheta$-close elements.
The underlying aim of this paper is first to state the cyclicversion of $\mathcal{J}$-integral Banach type contractive mappings introduced by Fallahi, Ghahramani and Soleimani Rad[Integral type contractions in partially ordered metric spaces and best proximity point, Iran. J. Sci. Technol. Trans. Sci. 44 (2020), 177-183] and second to show the existence of best proximity points for such contractive mappings in a metric space with a graph, which can entail a large number of former best proximity point results. One fundamental issue that can be distinguished between this work and previous researches is that it can also involve all of results stated by taking comparable and $\vartheta$-close elements.
[1] A. Abkar, M. Gabeleh, Best proximity points for cyclic mappings in ordered metric spaces, J. Optim Theory Appl. 151 (2011), 418-424.
[2] A. Abkar, M. Gabeleh, Generalized cyclic contractions in partially ordered metric spaces, Optim Lett. 6 (2012), 1819-1830.
[3] A. Aghanians A, K. Nourouzi, Fixed points of integral type contractions in uniform spaces. Filomat. 29 (7) (2015), 1613-1621.
[4] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133-181.
[5] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Sci. 29(9) (2002), 531-536.
[6] A. A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2006), 1001-1006.
[7] K. Fallahi, A. Aghanians, On quasi-contractions in metric spaces with a graph, Hacettepe J. Math. Stat. 45 (4) (2016), 1033-1047.
[8] K. Fallahi, G. Soleimani Rad, Best proximity point theorems in b-metric spaces endowed with a graph, Fixed Point Theory. 21 (2) (2020), 465-474.
[9] K. Fallahi, H. Ghahramani, G. Soleimani Rad, Integral type contractions in partially ordered metric spaces and best proximity point, Iran. J. Sci. Technol. Trans. Sci. 44 (2020), 177-183.
[10] K. Fallahi, G. Soleimani Rad, A. Fulga, Best proximity points for (φ − ψ)-weak contractions and some applications, Filomat. 37 (6) (2023), 1835-1842.
[11] J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 136 (4) (2008), 1359-1373.
[12] W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclic contractive conditions, Fixed Point Theory. 4 (1) (2003), 79-86.
[13] J. J. Nieto, R. Rodriguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order. 22 (3) (2005), 223-239.
[14] V. S. Raj, A best proximity point theorem for weakly contractive non-self mappings, Nonlinear Anal. 74 (2011), 4804-4808.
[15] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435-1443.
[16] B. E. Rhoades, A comparison of various definition of contractive mappings, Trans. Amer. Math. Soc. 266 (1977), 257-290.
[17] S. Sadiq Basha, Best proximity point theorems in the frameworks of fairly and proximally complete spaces, J. Fixed Point Theory Appl. 19 (3) (2017), 1939-1951.
[18] T. Suzuki, M. Kikkawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal. 71 (2009), 2918-2926.
