Common Fixed Points of Generalized α-Nonexpansive Multivalued Mappings via Modified S-Type Iteration
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Authors: R. SADHU AND C. NAHAK
DOI: 10.46793/KgJMat2406.951S
Abstract:
In this paper, we introduce a class of generalized α-nonexpansive multivalued mapping and study some of its important properties. In particular, this class is a multivalued version of the single-valued nonexpansive mapping, called generalized α-nonexpansive mapping proposed by Pant and Shukla [?]. A modified S-type iteration scheme is proposed to approximate the common fixed point of two multivalued mappings. Our algorithm provides a multivalued extension of the method given by Khan et al. [?]. Strong and weak convergence of the iterative process are also proved under suitable assumptions.
Keywords:
Multivalued mapping, common fixed point, S-iteration.
References:
[1] A. Abkar and M. Eslamian, Fixed point theorems for Suzuki generalized nonexpansive multivalued mappings in Banach spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 457935, 10 pages. https://doi.org/10.1155/2010/457935
[2] R. Agarwal, D. O Regan and D. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8(1) (2007), 61–79.
[3] S. S. Chang, R. P. Agarwal and L. Wang, Existence and convergence theorems of fixed points for multi-valued scc-, skc-, ksc-, scs- and c-type mappings in hyperbolic spaces, Fixed Point Theory Appl. 2015(83) (2015), 17 pages. https://doi.org/10.1186/s13663-015-0339-9
[4] S. S. Chang, Y. K. Tang, L. Wang, Y. G. Xu, Y. H. Zhao and G. Wang, Convergence theorems for some multivalued generalized nonexpansive mappings, Fixed Point Theory Appl. 2014(1) (2014), Article ID 33, 11 pages. https://doi.org/10.1186/1687-1812-2014-33
[5] J. S. Jung, Strong convergence theorems for multivalued nonexpansive nonself mappings in Banach spaces, Nonlinear Anal. 66(11) (2007), 2345–2354. https://doi.org/10.1016/j.na.2006.03.023
[6] S. H. Khan, Y. J. Cho and M. Abbas, Convergence to common fixed points by a modified iteration process, J. Appl. Math. Comput. 35(1) (2011), 607–616. https://doi.org/10.1007/s12190-010-0381-z
[7] S. H. Khan and I. Yildirim, Fixed points of multivalued nonexpansive mappings in Banach spaces, Fixed Point Theory Appl. 2012(73) (2012), Article ID 73, 9 pages. https://doi.org/10.1186/1687-1812-2012-73
[8] J. T. Markin, A fixed point theorem for set valued mappings, Bull. Amer. Math. Soc. 74(4) (1968), 639–640.
[9] S. B. Nadler, JR, Multivalued contraction mappings, Pac. J. Appl. Math. 30(2) (1969), 475–488.
[10] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73(4) (1967), 591–597.
[11] R. Pant and R. Shukla, Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 38(2) (2017), 248–266. https://doi.org/10.1080/01630563.2016.1276075
[12] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Aust. Math. Soc. 43(1) (1991), 153–159.
[13] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340(2) (2008), 1088–1095.
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