{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T16:07:58Z","timestamp":1772208478411,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,3,24]],"date-time":"2022-03-24T00:00:00Z","timestamp":1648080000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,24]],"date-time":"2022-03-24T00:00:00Z","timestamp":1648080000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100017170","name":"thailand science research and innovation","doi-asserted-by":"crossref","award":["64A306000005"],"award-info":[{"award-number":["64A306000005"]}],"id":[{"id":"10.13039\/501100017170","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2022,4]]},"DOI":"10.1007\/s40314-022-01821-6","type":"journal-article","created":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T02:02:33Z","timestamp":1648173753000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["On minimization and fixed point problems in Hadamard spaces"],"prefix":"10.1007","volume":"41","author":[{"given":"Sani","family":"Salisu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5463-4581","authenticated-orcid":false,"given":"Poom","family":"Kumam","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Songpon","family":"Sriwongsa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jamilu","family":"Abubakar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,3,24]]},"reference":[{"issue":"4","key":"1821_CR1","doi-asserted-by":"publisher","first-page":"1895","DOI":"10.1016\/j.na.2011.09.040","volume":"75","author":"A Abkar","year":"2012","unstructured":"Abkar A, Eslamian M (2012) Convergence theorems for a finite family of generalized nonexpansive multivalued mappings in CAT(0) spaces. Nonlinear Anal Theory Methods Appl 75(4):1895\u20131903","journal-title":"Nonlinear Anal Theory Methods Appl"},{"key":"1821_CR2","volume-title":"Gradient flows: in metric spaces and in the space of probability measures","author":"L Ambrosio","year":"2008","unstructured":"Ambrosio L, Gigli N, Savar\u00e9 G (2008) Gradient flows: in metric spaces and in the space of probability measures. Springer Science and Business Media, Berlin"},{"issue":"8","key":"1821_CR3","doi-asserted-by":"publisher","first-page":"4299","DOI":"10.1090\/S0002-9947-2014-05968-0","volume":"366","author":"D Ariza-Ruiz","year":"2014","unstructured":"Ariza-Ruiz D, Leu\u015ftean L, L\u00f3pez-Acedo G (2014) Firmly nonexpansive mappings in classes of geodesic spaces. Trans Am Math Soc 366(8):4299\u20134322","journal-title":"Trans Am Math Soc"},{"issue":"3","key":"1821_CR4","doi-asserted-by":"publisher","first-page":"1542","DOI":"10.1137\/140953393","volume":"24","author":"M Bac\u00e1k","year":"2014","unstructured":"Bac\u00e1k M (2014) Computing medians and means in Hadamard spaces. SIAM J Optim 24(3):1542\u20131566","journal-title":"SIAM J Optim"},{"key":"1821_CR5","unstructured":"Bacak M (2018) Old and new challenges in Hadamard spaces. arXiv preprint arXiv:1807.01355"},{"issue":"1","key":"1821_CR6","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s10711-008-9243-3","volume":"133","author":"ID Berg","year":"2008","unstructured":"Berg ID, Nikolaev IG (2008) Quasilinearization and curvature of Aleksandrov spaces. Geom Dedicata 133(1):195\u2013218","journal-title":"Geom Dedicata"},{"key":"1821_CR7","volume-title":"Metric spaces of non-positive curvature","author":"MR Bridson","year":"2013","unstructured":"Bridson MR, Haefliger A (2013) Metric spaces of non-positive curvature, vol 319. Springer Science and Business Media, Berlin"},{"key":"1821_CR8","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1007\/978-1-4612-1019-1_4","volume-title":"Buildings","author":"KS Brown","year":"1989","unstructured":"Brown KS (1989) Buildings. Buildings. Springer, Berlin, pp 76\u201398"},{"issue":"1","key":"1821_CR9","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/BF02715544","volume":"41","author":"F Bruhat","year":"1972","unstructured":"Bruhat F, Tits J (1972) Groupes r\u00e9ductifs sur un corps local. Publications Math\u00e9matiques de l\u2019Institut des Hautes \u00c9tudes Scientifiques 41(1):5\u2013251","journal-title":"Publications Math\u00e9matiques de l\u2019Institut des Hautes \u00c9tudes Scientifiques"},{"key":"1821_CR10","doi-asserted-by":"publisher","first-page":"5561","DOI":"10.22436\/jnsa.009.10.06","volume":"9","author":"S-S Chang","year":"2016","unstructured":"Chang S-S, Wu DP, Wang L, Wang G (2016) Proximal point algorithms involving fixed point of nonspreading-type multivalued mappings in Hilbert spaces. J Nonlinear Sci Appl 9:5561\u20135569","journal-title":"J Nonlinear Sci Appl"},{"issue":"1","key":"1821_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13663-016-0559-7","volume":"2016","author":"S-S Chang","year":"2016","unstructured":"Chang S-S, Yao J-C, Wang L, Qin LJ (2016) Some convergence theorems involving proximal point and common fixed points for asymptotically nonexpansive mappings in CAT(0) spaces. Fixed Point Theory Appl 2016(1):1\u201311","journal-title":"Fixed Point Theory Appl"},{"issue":"7","key":"1821_CR12","doi-asserted-by":"publisher","first-page":"1401","DOI":"10.1007\/s11590-014-0841-8","volume":"9","author":"P Cholamjiak","year":"2015","unstructured":"Cholamjiak P (2015) The modified proximal point algorithm in CAT(0) spaces. Optim Lett 9(7):1401\u20131410","journal-title":"Optim Lett"},{"issue":"1","key":"1821_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13663-015-0465-4","volume":"2015","author":"P Cholamjiak","year":"2015","unstructured":"Cholamjiak P, Abdou AA, Cho YJ (2015) Proximal point algorithms involving fixed points of nonexpansive mappings in CAT(0) spaces. Fixed Point Theory Appl 2015(1):1\u201313","journal-title":"Fixed Point Theory Appl"},{"key":"1821_CR14","doi-asserted-by":"crossref","unstructured":"Chaolamjiak W, Yambangwai D, Hammad HA (2021) Modified hybrid projection methods with SP iterations for quasi-nonexpansive multivalued mappings in Hilbert spaces. Bull Iran Math Soc 47:1399\u20131422","DOI":"10.1007\/s41980-020-00448-9"},{"key":"1821_CR15","unstructured":"Dehghan H, Rooin J (2014) Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces. arXiv preprint arXiv:1410.1137"},{"issue":"7","key":"1821_CR16","doi-asserted-by":"publisher","first-page":"975","DOI":"10.2989\/16073606.2019.1593255","volume":"43","author":"H Dehghan","year":"2020","unstructured":"Dehghan H, Izuchukwu C, Mewomo O, Taba D, Ugwunnadi G (2020) Iterative algorithm for a family of monotone inclusion problems in CAT(0) spaces. Quaest Math 43(7):975\u2013998","journal-title":"Quaest Math"},{"issue":"10","key":"1821_CR17","doi-asserted-by":"publisher","first-page":"2572","DOI":"10.1016\/j.camwa.2008.05.036","volume":"56","author":"S Dhompongsa","year":"2008","unstructured":"Dhompongsa S, Panyanak B (2008) On $$\\triangle $$-convergence theorems in CAT(0) spaces. Comput Math Appl 56(10):2572\u20132579","journal-title":"Comput Math Appl"},{"issue":"4","key":"1821_CR18","doi-asserted-by":"publisher","first-page":"762","DOI":"10.1016\/j.na.2005.09.044","volume":"65","author":"S Dhompongsa","year":"2006","unstructured":"Dhompongsa S, Kirk WA, Sims B (2006) Fixed points of uniformly Lipschitzian mappings. Nonlinear Anal Theory Methods Appl 65(4):762\u2013772","journal-title":"Nonlinear Anal Theory Methods Appl"},{"issue":"1","key":"1821_CR19","first-page":"35","volume":"8","author":"S Dhompongsa","year":"2007","unstructured":"Dhompongsa S, Kirk W, Panyanak B (2007) Nonexpansive set-valued mappings in metric and Banach spaces. J Nonlinear Convex Anal 8(1):35","journal-title":"J Nonlinear Convex Anal"},{"issue":"4","key":"1821_CR20","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.1007\/s11075-018-0521-3","volume":"80","author":"GZ Eskandani","year":"2019","unstructured":"Eskandani GZ, Raeisi M (2019) On the zero point problem of monotone operators in Hadamard spaces. Numer Algorithms 80(4):1155\u20131179","journal-title":"Numer Algorithms"},{"key":"1821_CR21","doi-asserted-by":"crossref","unstructured":"Feragen A, Hauberg S, Nielsen M, Lauze F (2011) Means in spaces of tree-like shapes. In: 2011 international conference on computer vision. IEEE, pp 736\u2013746","DOI":"10.1109\/ICCV.2011.6126311"},{"key":"1821_CR22","volume-title":"Uniform convexity, hyperbolic geometry, and nonexpansive mappings","author":"K Goebel","year":"1984","unstructured":"Goebel K, Simeon R (1984) Uniform convexity, hyperbolic geometry, and nonexpansive mappings. Dekker, London"},{"issue":"2","key":"1821_CR23","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1137\/0329022","volume":"29","author":"O G\u00fcler","year":"1991","unstructured":"G\u00fcler O (1991) On the convergence of the proximal point algorithm for convex minimization. SIAM J Control Optim 29(2):403\u2013419","journal-title":"SIAM J Control Optim"},{"key":"1821_CR24","doi-asserted-by":"crossref","unstructured":"Izuchukwu C, Aremu KO, Oyewole OK, Mewomo OT, Khan SH (2019) On Mixed Equilibrium Problems in Hadamard Spaces. J Math 2019, Article ID 3210649, 13 pages","DOI":"10.1155\/2019\/3210649"},{"issue":"1","key":"1821_CR25","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1007\/BF02566027","volume":"70","author":"J Jost","year":"1995","unstructured":"Jost J (1995) Convex functionals and generalized harmonic maps into spaces of non positive curvature. Commentarii Mathematici Helvetici 70(1):659\u2013673","journal-title":"Commentarii Mathematici Helvetici"},{"issue":"3","key":"1821_CR26","doi-asserted-by":"publisher","first-page":"1029","DOI":"10.1090\/S0002-9939-2012-11743-5","volume":"141","author":"B Kakavandi","year":"2013","unstructured":"Kakavandi B (2013) Weak topologies in complete $$CAT(0)$$ metric spaces. Proc Am Math Soc 141(3):1029\u20131039","journal-title":"Proc Am Math Soc"},{"issue":"3","key":"1821_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11784-020-00796-3","volume":"22","author":"MAA Khan","year":"2020","unstructured":"Khan MAA, Cholamjiak P (2020) A multi-step approximant for fixed point problem and convex optimization problem in Hadamard spaces. J Fixed Point Theory Appl 22(3):1\u201317","journal-title":"J Fixed Point Theory Appl"},{"key":"1821_CR28","unstructured":"Khatibzadeh H, Mohebbi V (2016) Monotone and pseudo-monotone equilibrium problems in Hadamard spaces. arXiv preprint arXiv:1611.01829"},{"issue":"4","key":"1821_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/S1687182004406081","volume":"2004","author":"W Kirk","year":"2004","unstructured":"Kirk W (2004) Fixed point theorems in spaces and-trees. Fixed Point Theory Appl 2004(4):1\u20138","journal-title":"Fixed Point Theory Appl"},{"issue":"12","key":"1821_CR30","doi-asserted-by":"publisher","first-page":"3689","DOI":"10.1016\/j.na.2007.04.011","volume":"68","author":"W Kirk","year":"2008","unstructured":"Kirk W, Panyanak B (2008) A concept of convergence in geodesic spaces. Nonlinear Anal Theory Methods Appl 68(12):3689\u20133696","journal-title":"Nonlinear Anal Theory Methods Appl"},{"key":"1821_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-10927-5","volume-title":"Fixed point theory in distance spaces","author":"W Kirk","year":"2014","unstructured":"Kirk W, Shahzad N (2014) Fixed point theory in distance spaces. Springer, Berlin"},{"key":"1821_CR32","unstructured":"Kumam P, Chaipunya P (2018) Equilibrium problems and proximal algorithms in Hadamard spaces. arXiv preprint arXiv:1807.10900"},{"issue":"7\u20138","key":"1821_CR33","doi-asserted-by":"publisher","first-page":"899","DOI":"10.1007\/s11228-008-0102-z","volume":"16","author":"P-E Maing\u00e9","year":"2008","unstructured":"Maing\u00e9 P-E (2008) Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set-Valued Anal 16(7\u20138):899\u2013912","journal-title":"Set-Valued Anal"},{"issue":"3","key":"1821_CR34","first-page":"154","volume":"4","author":"B Martinet","year":"1970","unstructured":"Martinet B (1970) Br\u00e8ve communication. r\u00e9gularisation d\u2019in\u00e9quations variationnelles par approximations successives. Revue fran\u00e7aise d\u2019informatique et de recherche op\u00e9rationnelle S\u00e9rie rouge 4(3):154\u2013158","journal-title":"Revue fran\u00e7aise d\u2019informatique et de recherche op\u00e9rationnelle S\u00e9rie rouge"},{"issue":"2","key":"1821_CR35","doi-asserted-by":"publisher","first-page":"199","DOI":"10.4310\/CAG.1998.v6.n2.a1","volume":"6","author":"UF Mayer","year":"1998","unstructured":"Mayer UF (1998) Gradient flows on nonpositively curved metric spaces and harmonic maps. Comm Anal Geom 6(2):199\u2013253","journal-title":"Comm Anal Geom"},{"issue":"2","key":"1821_CR36","first-page":"113","volume":"5","author":"A Mebawondu","year":"2019","unstructured":"Mebawondu A (2019) Proximal point algorithms for finding common fixed points of a finite family of nonexpansive multivalued mappings in real Hilbert spaces. Khayyam J Math 5(2):113\u2013123","journal-title":"Khayyam J Math"},{"issue":"3","key":"1821_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11784-018-0590-x","volume":"20","author":"W Phuengrattana","year":"2018","unstructured":"Phuengrattana W, Tiammee J (2018) Proximal point algorithms for finding common fixed points of a finite family of quasi-nonexpansive multi-valued mappings in real Hilbert spaces. J Fixed Point Theory Appl 20(3):1\u201314","journal-title":"J Fixed Point Theory Appl"},{"issue":"6","key":"1821_CR38","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1016\/0362-546X(90)90058-O","volume":"15","author":"S Reich","year":"1990","unstructured":"Reich S, Shafrir I (1990) Nonexpansive iterations in hyperbolic spaces. Nonlinear Anal Theory Methods Appl 15(6):537\u2013558","journal-title":"Nonlinear Anal Theory Methods Appl"},{"issue":"5","key":"1821_CR39","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"RT Rockafellar","year":"1976","unstructured":"Rockafellar RT (1976) Monotone operators and the proximal point algorithm. SIAM J Control Optim 14(5):877\u2013898","journal-title":"SIAM J Control Optim"},{"issue":"1","key":"1821_CR40","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1080\/10556788.2016.1219908","volume":"32","author":"R Suparatulatorn","year":"2017","unstructured":"Suparatulatorn R, Cholamjiak P, Suantai S (2017) On solving the minimization problem and the fixed-point problem for nonexpansive mappings in CAT(0) spaces. Optim Methods Softw 32(1):182\u2013192","journal-title":"Optim Methods Softw"},{"issue":"1","key":"1821_CR41","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1112\/S0024610702003332","volume":"66","author":"H-K Xu","year":"2002","unstructured":"Xu H-K (2002) Iterative algorithms for nonlinear operators. J Lond Math Soc 66(1):240\u2013256","journal-title":"J Lond Math Soc"},{"issue":"6","key":"1821_CR42","first-page":"1939","volume":"43","author":"G Zamani Eskandani","year":"2017","unstructured":"Zamani Eskandani G, Azarmi S, Eslamian M (2017) Composition of resolvents and quasi-nonexpansive multivalued mappings in Hadamared spaces. Bull Iran Math Soc 43(6):1939\u20131955","journal-title":"Bull Iran Math Soc"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01821-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-022-01821-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01821-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T18:11:44Z","timestamp":1650305504000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-022-01821-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,24]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["1821"],"URL":"https:\/\/doi.org\/10.1007\/s40314-022-01821-6","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,24]]},"assertion":[{"value":"1 August 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 January 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 January 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"117"}}