A New Iterative Scheme for Approximating Fixed Points of Suzuki Generalized Multivalued Nonexpansive Mappings

In this paper, we study to approximate fixed points of Suzuki generalized multivalued nonexpansive mappings by using a three-step iterative scheme (1.1) introduced in [17]. We establish some weak and strong convergence results for mappings satisfying condition (C) with the newly proposed iterative scheme in the framework of uniformly convex real Banach spaces.

___

  • [1] Nadler, S.B., "Multivalued contraction mappings", Pacific J. Math. 30(2) (1969) : 475-488.
  • [2] Markin, J.T., "A fixed point theorem for set valued mappings", Bull. Amer. Math. Soc. 74(4) (1968) : 545-547.
  • [3] Abkar, A., Eslamian, M., "Fixed point theorems for Suzuki generalized nonexpansive multivalued mappings in Banach spaces", Fixed Point Theory and Applications 2010 (2010) : 1-10.
  • [4] Yildirim, I., "On convergence of an implicit algorithm for multivalued mappings in Banach spaces", Miskolc Mathematical Notes 15(2) (2014) : 771-780.
  • [5] Thakur, B.S., Thakur, D., Postolache, M., "A new iterative scheme for numerical reckoning fixed points of Suzuki's generalized nonexpansive mappings", Applied Mathematics and Computation 275 (2016) : 147-155.
  • [6] Opial,Z., "Weak convergence of the sequence of successive approximations for nonexpansive mappings", Bull Amer. Math. Soc. 73 (1967) : 591-597.
  • [7] Eslamian, M., Abkar, A., "One-step iterative process for a finite family of multivalued mappings", Mathematical and Computer Modelling, 54 (2011) : 105-111.
  • [8] Garcia-Falset, J., Lorens-Fusters, E., Suzuki, T., "Fixed point theory for a class of generalized nonexpansive mappings", J.Math. Anal. Appl. 375 (2011) : 185-195.
  • [9] Kaewchareon, A., Panyanak, B., "Fixed point theorems for some generalized multivalued nonexpansive mappings", Nonlinear Analysis, 74 (2011) : 5578-5584.
  • [10] Ali, J., Ali, F., Kumar, P., "Approximation of fixed points for Suzuki's generalized nonexpansive mappings", Mathematics 7(6) (2019) : 522.
  • [11] Yildirim, I., "Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C)", Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 (2017) : 51-65.
  • [12] Phuengrattana, W., "Approximating fixed points of Suzuki-generalized nonexpansive mappings", Nonlinear Anal. Hybrid Syst. 5(3) (2011) : 583-590.
  • [13] Akkasriworn, N., Sokhuma, K., Chuikamwong, K., "Ishikawa iterative process for a pair of Suzuki generalized nonexpansive single valued and multivalued mappings in Banach spaces , Int. J. Math. Anal. 6(19) (2012) : 923-932.
  • [14] Schu, J., "Weak and strong convergence to fixed points of asymptotically nonexpansive mappings", Bull. Aust. Math. Soc. 43 (1991) : 153-159.
  • [15] Suzuki, T., "Fixed point theorems and convergence theorems for some generalized nonexpansive mappings", J. Math. Anal. Appl. 340(2) (2008) : 1088-1095.
  • [16] Abkar, A., Eslamian, M., "Convergence theorems for a finite family of generalized nonexpansive multivalued mappings in CAT (0) spaces" Nonlinear Analysis: Theory, Methods & Applications 75(4) (2012) : 1895-1903.
  • [17] Kaplan, M., Kopuzlu, A., "Three-step iterative scheme for Approximating fixed points of multivalued nonexpansive mappings", Advances in Fixed Point Theory 3(2) (2013) : 273-285.
  • [18] Sadhu, R., Majee, P., Nahak, C., "Fixed point theorems on generalized -nonexpansive multivalued mappings", The Journal of Analysis 29 (2021) : 1165-1190.
  • [19] Ullah, K., Arshad, M., "Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process", Filomat, 32(1) (2018) : 187-196.
  • [20] Khan, S. H., Yildirim, I., "Fixed points of multivalued nonexpansive mappings in Banach spaces", Fixed Point Theory Appl. (2012) : 73.