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.
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.
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.
Kaplan Özekes, M. (2024). Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces. Turkish Journal of Mathematics and Computer Science, 16(1), 21-27. https://doi.org/10.47000/tjmcs.1261727
AMA
Kaplan Özekes M. Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces. TJMCS. June 2024;16(1):21-27. doi:10.47000/tjmcs.1261727
Chicago
Kaplan Özekes, Makbule. “Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces”. Turkish Journal of Mathematics and Computer Science 16, no. 1 (June 2024): 21-27. https://doi.org/10.47000/tjmcs.1261727.
EndNote
Kaplan Özekes M (June 1, 2024) Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces. Turkish Journal of Mathematics and Computer Science 16 1 21–27.
IEEE
M. Kaplan Özekes, “Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces”, TJMCS, vol. 16, no. 1, pp. 21–27, 2024, doi: 10.47000/tjmcs.1261727.
ISNAD
Kaplan Özekes, Makbule. “Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces”. Turkish Journal of Mathematics and Computer Science 16/1 (June 2024), 21-27. https://doi.org/10.47000/tjmcs.1261727.
JAMA
Kaplan Özekes M. Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces. TJMCS. 2024;16:21–27.
MLA
Kaplan Özekes, Makbule. “Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 1, 2024, pp. 21-27, doi:10.47000/tjmcs.1261727.
Vancouver
Kaplan Özekes M. Aprroximation of Endpoints for Generalized $\alpha $-Nonexpansive Multivalued Mappings in Hyperbolic Spaces. TJMCS. 2024;16(1):21-7.