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Optimization Methods and Software Volume 32, 2017 - Issue 1
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Original Articles

On solving the minimization problem and the fixed-point problem for nonexpansive mappings in CAT(0) spaces

Raweerote SuparatulatornSchool of Science, University of Phayao, Phayao56000, ThailandView further author information
,
Prasit CholamjiakSchool of Science, University of Phayao, Phayao56000, ThailandCorrespondence[email protected]
View further author information
&
Suthep SuantaiDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai50200, ThailandView further author information
Pages 182-192 | Received 26 Oct 2015, Accepted 27 Jul 2016, Published online: 29 Sep 2016

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Sani Salisu, Poom Kumam & Songpon Sriwongsa. (2023) A viscosity-type scheme for optimization problems in Hadamard spaces with applications. Optimization 0:0, pages 1-25.
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Satit Saejung & Pongsakorn Yotkaew. (2021) Convergence theorems for asymptotically quasi-nonexpansive sequences with applications. Optimization 70:10, pages 2193-2225.
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Nopparat Wairojjana, Nuttapol Pakkaranang, Izhar Uddin, Poom Kumam & Aliyu Muhammed Awwal. (2020) Modified proximal point algorithms involving convex combination technique for solving minimization problems with convergence analysis. Optimization 69:7-8, pages 1655-1680.
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Phatiphat Thounthong, Nuttapol Pakkaranang, Yeol Je Cho, Wiyada Kumam & Poom Kumam. (2020) The numerical reckoning of modified proximal point methods for minimization problems in non-positive curvature metric spaces. International Journal of Computer Mathematics 97:1-2, pages 245-262.
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C. C. Okeke & C. Izuchukwu. (2019) A strong convergence theorem for monotone inclusion and minimization problems in complete CAT(0) spaces. Optimization Methods and Software 34:6, pages 1168-1183.
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Lucas Wangwe. (2023) Fixed point theorems for interpolative Ćirić-type contraction mappings in CAT (0) space with application to hyperbolical rotation matrix. The Journal of Analysis 31:4, pages 2777-2798.
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Kanokwan Kratuloek, Poom Kumam, Kittisak Amnuaykarn, Jamnian Nantadilok & Sani Salisu. (2023) Iterative approximation of common fixed points of two nonself asymptotically nonexpansive mappings in CAT(0) spaces with numerical examples. Mathematical Methods in the Applied Sciences 46:12, pages 13521-13539.
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K. O. Aremu, C. Izuchukwu, G. N. Ogwo & O. T. Mewomo. (2023) A modified viscosity iterative method for implicit midpoint rule for optimization and fixed point problems in CAT(0) spaces. Afrika Matematika 34:2.
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Sani Salisu, Poom Kumam & Songpon Sriwongsa. (2023) Convergence theorems for monotone vector field inclusions and minimization problems in Hadamard spaces. Analysis and Geometry in Metric Spaces 11:1.
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G. N. Ogwo, H. A. Abass, C. Izuchukwu & O. T. Mewomo. (2022) Modified Proximal Point Methods Involving Quasi-pseudocontractive Mappings in Hadamard Spaces. Acta Mathematica Vietnamica 47:4, pages 847-873.
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Sani Salisu, Poom Kumam, Songpon Sriwongsa & Jamilu Abubakar. (2022) On minimization and fixed point problems in Hadamard spaces. Computational and Applied Mathematics 41:3.
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Abebe Regassa Tufa & Habtu Zegeye. (2021) Approximating common fixed points of a family of non-self mappings in CAT(0) spaces. Boletín de la Sociedad Matemática Mexicana 28:1.
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Chainarong Khunpanuk, Chanchal Garodia, Izhar Uddin & Nuttapol Pakkaranang. (2022) On a proximal point algorithm for solving common fixed point problems and convex minimization problems in Geodesic spaces with positive curvature. AIMS Mathematics 7:5, pages 9509-9523.
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Sirous Moradi & Mohsen Tahernia. (2022) Minimization problem of proximal point algorithm in complete CAT(0) spaces. Filomat 36:18, pages 6289-6298.
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Sabiya Khatoon, Izhar Uddin & Metin Basarir. (2021) A modified proximal point algorithm for a nearly asymptotically quasi-nonexpansive mapping with an application. Computational and Applied Mathematics 40:7.
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Thidaporn Seangwattana, Somyot Plubtieng & Kanokwan Sitthithakerngkiet. (2021) A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems. Indian Journal of Pure and Applied Mathematics 52:2, pages 614-628.
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K. O. Aremu, C. Izuchukwu, A. A. Mebawondu & O. T. Mewomo. (2020) A viscosity-type proximal point algorithm for monotone equilibrium problem and fixed point problem in an Hadamard space. Asian-European Journal of Mathematics 14:04, pages 2150058.
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G. C. Ugwunnadi, O. C. Collins, V. M. Magagula & A. R. Khan. (2020) Monotone inclusion problem and fixed point problem of a generalized demimetric mapping in CAT(0) spaces. Rendiconti del Circolo Matematico di Palermo Series 2 70:1, pages 365-387.
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Izhar Uddin, Sabiya Khatoon, Nabil Mlaiki & Thabet Abdeljawad. (2021) A modified iteration for total asymptotically nonexpansive mappings in Hadamard spaces. AIMS Mathematics 6:5, pages 4758-4770.
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Muhammad Aqeel Ahmad Khan & Prasit Cholamjiak. (2020) A multi-step approximant for fixed point problem and convex optimization problem in Hadamard spaces. Journal of Fixed Point Theory and Applications 22:3.
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Hafiz Fukhar-ud-din & Abdul Rahim Khan. (2019) Strong and $$\triangle $$-convergence of Moudafi’s iterative algorithm for generalized nonexpansive mappings in convex metric spaces. Rendiconti del Circolo Matematico di Palermo Series 2 69:2, pages 547-559.
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C. Izuchukwu, A. A. Mebawondu, K. O. Aremu, H. A. Abass & O. T. Mewomo. (2019) Viscosity iterative techniques for approximating a common zero of monotone operators in an Hadamard space. Rendiconti del Circolo Matematico di Palermo Series 2 69:2, pages 475-495.
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Aree Varatechakongka & Withun Phuengrattana. (2019) A study on fixed point theorems for a class of generalized nonexpansive mappings in Hadamard spaces. Boletín de la Sociedad Matemática Mexicana 26:2, pages 687-699.
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Shih-sen Chang, L. Wang, X. R. Wang & L. C. Zhao. (2020) Common solution for a finite family of minimization problem and fixed point problem for a pair of demicontractive mappings in Hadamard spaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 114:2.
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Suthep Suantai, Kunrada Kankam & Prasit Cholamjiak. (2020) A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces. Mathematics 8:1, pages 42.
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E.E.A. Batista, G.C. Bento & O.P. Ferreira. (2020) An extragradient-type algorithm for variational inequality on Hadamard manifolds. ESAIM: Control, Optimisation and Calculus of Variations 26, pages 63.
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Phatiphat Thounthong, Nuttapol Pakkaranang, Phachara Saipara, Pawicha Phairatchatniyom & Poom Kumam. (2019) Convergence analysis of modified iterative approaches in geodesic spaces with curvature bounded above. Mathematical Methods in the Applied Sciences 42:17, pages 5929-5943.
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Wiyada Kumam, Duangkamon Kitkuan, Anantachai Padcharoen & Poom Kumam. (2019) Proximal point algorithm for nonlinear multivalued type mappings in Hadamard spaces. Mathematical Methods in the Applied Sciences 42:17, pages 5758-5768.
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Chinedu Izuchukwu, Kazeem Olalekan Aremu, Olawale Kazeem Oyewole, Oluwatosin Temitope Mewomo & Safeer Hussain Khan. (2019) On Mixed Equilibrium Problems in Hadamard Spaces. Journal of Mathematics 2019, pages 1-13.
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Godwin C. Ugwunnadi, Chinedu Izuchukwu & Oluwatosin T. Mewomo. (2019) Proximal point algorithm involving fixed point of nonexpansive mapping in 𝑝-uniformly convex metric space. Advances in Pure and Applied Mathematics 10:4, pages 437-446.
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C. Izuchukwu, K. O. Aremu, A. A. Mebawondu & O. T. Mewomo. (2019) A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space. Applied General Topology 20:1, pages 193.
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G. Zamani Eskandani & M. Raeisi. (2018) On the zero point problem of monotone operators in Hadamard spaces. Numerical Algorithms 80:4, pages 1155-1179.
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Shih-sen Chang, Jen-Chih Yao, Ching-Feng Wen & Lin Wang. (2018) A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces. Journal of Inequalities and Applications 2018:1.
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Nuttapol Pakkaranang, Poom Kumam & Yeol Je Cho. (2017) Proximal point algorithms for solving convex minimization problem and common fixed points problem of asymptotically quasi-nonexpansive mappings in CAT(0) spaces with convergence analysis. Numerical Algorithms 78:3, pages 827-845.
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Withun Phuengrattana, Nawitcha Onjai-uea & Prasit Cholamjiak. (2018) Modified Proximal Point Algorithms for Solving Constrained Minimization and Fixed Point Problems in Complete CAT(0) Spaces. Mediterranean Journal of Mathematics 15:3.
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