Approximation of endpoints for multi-valued mappings in metric spaces

Journal of Linear and Topological Algebra

مقاله 4، دوره 09، شماره 02، شهریور 2020، صفحه 129-137   

نوع مقاله: Research Paper

نویسندگان

K. Ullah؛ J. Ahmad^* ؛ N. Muhammad

Department of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkha, Pakistan

چکیده

In this paper, under some appropriate conditions, we prove some $\Delta$ and strong convergence theorems of endpoints for multi-valued nonexpansive mappings using modified Agarwal-O'Regan-Sahu iterative process in the general setting of 2-uniformly convex hyperbolic spaces. Our results extend and unify some recent results of the current literature.

کلیدواژه‌ها

Endpoint؛ condition (J)؛ $Delta$-convergence؛ strong convergence؛ hyperbolic space

مراجع

[1] T. Abdeljawad, K. Ullah, J. Ahmad, N. Mlaiki, Iterative approximation of endpoints for multivalued mappings in Banach spaces, J. Funcion Space. (2020), 2020:2179059.

[2] N. Akkasriworn, K. Sokhuma, S-iterative process for a pair of single valued and multi-valued mappings in Banach spaces, Thai J. Math. 14 (2016), 21-30.

[3] J. P. Aubin, J. Siegel, Fixed points and stationary points of dissipative multivalued maps, Proc. Am. Math. Soc. 78 (1980), 391-398.

[4] F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. USA. 54 (1965), 1041-1044.

[5] L. Chen, L. Gao, D. Chen, Fixed point theorems of mean nonexpansive setvalued mappings in Banach spaces, J. Fixed Point Theory Appl. 19 (2017), 2129-2143.

[6] P. Chuadchawna, A. Farajzadeh, A. Kaewcharoen, Convergence theorems and approximating endpoints for multivalued Suzuki mappings in hyperbolic spaces, J. Comp. Anal. Appl. 28 (2020), 903-916.

[7] R. Espinola, M. Hosseini, K. Nourouzi, On stationary points of nonexpansive set-valued mappings, Fixed Point Theory Appl. 236 (2015), 1-13.

[8] D. Gohde, Zum Prinzip der Kontraktiven Abbildung, Math. Nachr. 30 (1965), 251-258.

[9] M. Hosseini, K. Nourouzi, D. O’Regan, Stationary points of set-valued contractive and nonexpansive mappings on ultrametric spaces, Fixed Point Theory 19 (2) (2018), 587-594.

[10] M. A. Khamsi, A. R. Khan, Inequalities in metric spaces with applications, Nonlinear Anal. 74 (2011),
4036-4045.

[11] W. A. Kirk, A fixed point theorem for mappings which do not increase distance, Am. Math. Monthly. 72 (1965), 1004-1006.

[12] T. Laokul, B. Panynak, A generalization of the (CN) inequality and its applications, Carpathian J. Math. 36 (1) (2020), 81-90.

[13] L. Leustean, A quadratic rate of asymptotic regularity for CAT(0) spaces, J. Math. Anal. Appl. 325 (2007), 386-399.

[14] T. C. Lim, A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach spaces, Bull. Am. Math. Soc. 80 (1974), 1123-1126.

[15] B. Panyanak, Approximating endpoints of multi-valued nonexpansive mappings in Banach spaces, J. Fixed Point Theory Appl. 20 (2018), 1-8.

[16] B. Panyanak, Endpoints of multivalued nonexpansive mappings in geodesic spaces, Fixed Point Theory Appl. 147 (2015), 1-11.

[17] B. Panyanak, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comput. Math. Appl. 54 (2007), 872-877.

[18] S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital. 5 (1972), 26-42.

[19] K. P. R. Sastry, G. V. R. Babu, Convergence of Ishikawa iterates for a multivalued mapping with a fixed point, Czechoslovak Math. J. 55 (2005), 817-826.

[20] S. Saejung, Remarks on endpoints of multivalued mappings in geodesic spaces, Fixed Point Theory Appl. 52 (2016), 1-12.

[21] N. Shahzad, H. Zegeye, On Mann and Ishikawa iteration schemes for multivalued maps in Banach spaces, Nonlinear Anal. 71 (2009), 838-844.

[22] K. Sokhuma, On the S-iteration processes for multivalued mappings in some CAT(κ) spaces, Int. J. Math. Anal. 8 (18) (2014), 857-864.

[23] K. Sokhuma, S-iterative process for a pair of single valued and multi-valued nonexpansive mappings, Int. Math. Form. 7 (2012), 839-847.

[24] S. Sopha, W. Phuengrattana, Convergence of the S-iteration process for a pair of single-valued and multi-valued generalized nonexpansive mappings in CAT(κ) spaces, Thai J. Math. 13 (2015), 627-640.

[25] Y. Song, Y. J. Cho, Some notes on Ishikawa iteration for multi-valued mappings, Bull. Korean Math. Soc. 48 (2011), 575-584.

[26] Y. Song, H. Wang, Erratum to “Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces”, Comput. Math. Appl. 52 (2008), 2999-3002.

[27] K. Ullah, M. S. U. Khan, N. Muhammad, J. Ahmad, Approximation of endpoints for multivalued nonexpansive mappings in geodesic spaces, Asian-European J. Math. (2019), 2019:2050141.

[28] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16 (1991), 1127-1138.