Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces

Yıl 2024, , 21 - 27, 30.06.2024

Makbule Kaplan Özekes

https://doi.org/10.47000/tjmcs.1261727

Öz

In this paper, we establish that the sequence of the new iteration converges to an endpoints of multivalued generalized α-nonexpansive mappings in 2-uniformly convex hyperbolic space. We present some strong and Δ-convergence theorems for such operator in a hyperbolic metric space. The results presented in this paper extend and improve some recent results in the literature.

Anahtar Kelimeler

Generalized $\alpha $-nonexpansive mapings, strong and $\Delta $-convergence, hyperbolic space, multivalued mappings

Kaynakça

• Abdeljawad, T., Ullah, K., Ahmad, J., Mlaiki, N., Iterative approximation of endpoints for multivalued mappings in Banach spaces, Hindawi Journal of Function Spaces, 2020(2020), Article ID 2179059.
• Abkar, A., Eslamian, M., A fixed point theorem for generalized nonexpansive multivalued mappings, Fixed Point Theory, 12(2)(2011), 241–246.
• Chuadchawna, P., Farajzadeh, A., Kaewchareon, A., Convergence theorems and approximating endpoints for multivalued Suzuki mappings in hyperbolic spaces, Journal of Computational Analysis and Applications, 28(2020), 903–916.
• Dhompongsa, S., Panyanak, B., On Δ-convergence theorems in CAT(0) space, Comput. Math. Appl., 56(2008), 2572–2579.
• Iqbal, H., Abbas, M., Husnine, S.M., Existence and approximation of fixed points of multivalued generalized α-nonexpansive mappings in Banach spaces, Numerical Algorithms, 85(2020), 1029–1049.
• Kaplan, M., Iterative approximation of endpoints for Suzuki Generalized multivalued mappings in Hadamard spaces, JP Journal of Fixed Point Theory and Applications, 15(3)(2020), 125–139.
• Kohlenbach, U., Some logical metatheorems with applications in functional analysis, Transactions of the American Mathematical Society, 357(1)(2005), 89–128.
• Kudtha, A., Panyanak, B., Common endpoints for Suzuki mappings in uniformly convex hyperbolic spaces, Thai J. Math , (special issue), (2018), 159–168.
• Laokul, T., Panyanak, B., A generalizzation of the (CN) inequality and its applications, Carpathian Journal of Mathematics, 36(1)(2020), 81–90.
• Leustean, L., A quadratic rate of asymptotic regularity for CAT(0) spaces, J. Math. Anal. Appl., 325(2007), 386–399.
• Nanjaras, B., Panyanak, B., Phuengrattana,W., Fixed point theorems and convergence theorems for suzuki-generalized nonexpansive mappings in CAT(0) spaces, Nonlinear Anal. Hybrid Syst., 4(1)(2010), 25–31.
• Pant, R., Shukla, R., Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces, Numerical Functional Analysis and Optimization, 38(2)(2017), 248–266.
• Panyanak, B., Endpoints of multivalued nonexpansive mappings in geodesic spaces, Fixed Point Theory Appl., 147(2015), 1–11.
• Panyanak, B., Approximating endpoints of multi-valued nonexpansive mappings in Banach spaces, J. Fixed Point Theory Appl., 20(2018), 1–8.
• Panyanak, B., Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comp. Math. Appl., 54(6)(2007), 872–877.
• Sadhu, R., Majee, P., Nahak, C., Fixed point theorems on generalized α-nonexpansive multivalued mappings, The Journal of Analysis, 29(2021), 1165–1190.
• Sastry, K.P.R., Babu, G.V.R., Convergence of Ishikawa iterates for a multivalued mapping with a fixed point, Czechoslovak Math. J., 55(2005), 817–826.
• Saejung, S., Remarks on endpoints of multivalued mappings on geodesic spaces, Fixed Point Theory Appl., 52(2016), 1–12.
• Shahzad, N., Zegeye, H., On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Analysis, 71(2009), 838–844.
• Song, Y., Wang, H., Erratum to ‘Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comp. Math. Appl., 55(12)(2008), 2999–3002.
• Suzuki, T., Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl., 340(2008), 1088–1095.
• Uddin, I., Agarwal, S., Abdou, A.A., Approximation of endpoints for α−Reich–Suzuki nonexpansive mappings in hyperbolic metric spaces, Mathematics, 9(14)(2021), 1692.
• Ullah, K., Ahmad, J., Mlaiki, N., On Noor iterative process for multi-valued nonexpansive mappings with application, International Journal of Mathematical Analysis, 13(6)(2019), 293–307.
• Ullah, K., Khan, M.S.U., Muhammad, N., Ahmad, J., Approximation of endpoints for multivalued nonexpansive mappings in geodesic spaces, Asian-European Journal of Mathematics, (2019) article 2050141.
• Ullah, K., Ahmad, J., Muhammad, N., Approximation of endpoints for multivalued mappings in metric spaces, Journal of Linear and Topological Algebra, 9(2)(2020), 129–137.