Fixed point of multi-valued Zamfirescu operator and convergence results in modular metric spaces endowed with graph

[1] A. A. Abdou and M.A. Khamsi, Fixed points of multi-valued contraction mappings in modular metric spaces, Fixed Point Theory and Applications, 2014 (2014), 1-10.
[2] S. Alawa, A. Pariya, N. Asthana and P. Pathak, Common fixed point of Kannan and weak contractive type mappings on a modular metric space endowed with a graph, Journal of Mathematics and Computer Science, 11(6) (2021), 7793-7804.
[3] J. Ali. and F. Ali, A new iterative scheme to approximate fixed points and the solution of a delay differential equation, Journal of Nonlinear Convex Analysis, 21(9) (2020), 2151-2163.
[4] G. V. R. Babu and K. N. V. V. Prasad, Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators, Fixed Point Theory and Applications, 2006 (2006), 1–6.
[5] S. Banach, Sur les operations dans ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae, 3 (1922), 133-181.
[6] V. Berinde, A convergence theorem for Mann iteration in the class of Zamfirescu operators, Analele Universitat¸ii de Vest, Timi¸soara Seria Matematica–Informatica XLV, 1 (2007), 33–41.
[7] S. K. Chatterjea, Fixed point theorems, Comptes Rendus de l’Academie Bulgare des Sciences, 25 (1972), 727–730.
[8] V. V. Chistyako, Modular metric spaces, I:basic concepts, Nonlinear Analysis: Theory, Methods and Applications, 72(1) (2010), 1-14.
[9] F. A. Echenique, Short and constructive proof of Tarski’s fixed point theorem, International Journal of Game Theory, 33(2) (2005), 215-218.
[10] R. Espinola and W.A. Kirk, Fixed point theorems in R− trees with applications to graph theory, Topology and its Applications, 153 (2006), 1046-1055.
[11] S. George and P. Shaini, Convergence Theorems for the Class of Zamfirescu Operator, International Mathematical Forum, 7(36) (2012), 1785 - 1792.
[12] A. Kaewkhao and K. Neammanee, Fixed point theorems of multi-valued Zamfirescu mapping, Journal of Mathematics Research, 2(2) (2010), 1-7.
[13] R. Kannan, Some results on fixed points, Bulletin of the Calcutta Mathematical Society, 60 (1968), 71–76.
[14] J. K. Kim, S. Dashputre and W.H. Lim, Approximation of fixed points for multi-valued nonexpansive mappings in Banach space, Global Journal of Pure and Applied Mathematics, 12(6) (2016), 4901-4912.
[15] W. M. Kowzslowski, Modular function spaces, Monographs and text books in pure and applied mathematics, 122, Marcel Dekker, Inc., New York, 1988.
[16] P. Kumam, Fixed point theorems for nonexpansive mapping in modular spaces, Archivum Mathematicum, 40 (2004), 345-353.
[17] J. T. Markin, Continuous dependence of fixed point sets, Proceedings of American Mathematical Society, 38 (1973), 545-547.
[18] S. B. Nadler, Multi-valued contraction mappings, Pacific Journal of Mathematics, 30(2) (1969), 475–488. 
[19] H. Nakano, Modulered semi-ordered linear spaces, Maruzen Cooperation Limited, Tokyo, 1950.
[20] Y. Qing and B. E. Rhodes, Comments on the Rate of Convergence between Mann and Ishikawa Iterations Applied to Zamfirescu Operators, Fixed Point Theory and Applications, 2008 (2008), 1-3.
[21] J. Tiammee, A. Kaewkhao and S. Suantai, On Browder’s convergence theorem and Halpern iteration process for G− nonexpansive mappings in Hilbert spaces endowed with graphs, Fixed Point Theory and Applications, 187 (2015), 1-12.
[22] T. Zamfirescu, Fixed point theorems in metric spaces, Archiv der Mathematik, 23 (1972), 292–298.