{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T19:41:39Z","timestamp":1761766899871,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,2]],"date-time":"2021-04-02T00:00:00Z","timestamp":1617321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003086","name":"Basque Government","doi-asserted-by":"publisher","award":["Grant IT1207-19."],"award-info":[{"award-number":["Grant IT1207-19."]}],"id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we present some fixed point results for a class of nonexpansive type and \u03b1-Krasnosel\u2019ski\u012d mappings. Moreover, we present some convergence results for one parameter nonexpansive type semigroups. Some non-trivial examples have been presented to illustrate facts.<\/jats:p>","DOI":"10.3390\/sym13040585","type":"journal-article","created":{"date-parts":[[2021,4,2]],"date-time":"2021-04-02T04:13:51Z","timestamp":1617336831000},"page":"585","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Fixed Point Theorems for Nonexpansive Type Mappings in Banach Spaces"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9990-2298","authenticated-orcid":false,"given":"Rajendra","family":"Pant","sequence":"first","affiliation":[{"name":"Department of Mathematics &amp; Applied Mathematics, Kingsway Campus, University of Johannesburg, Auckland Park 2006, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0438-4366","authenticated-orcid":false,"given":"Prashant","family":"Patel","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Applied Mathematics, Kingsway Campus, University of Johannesburg, Auckland Park 2006, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9835-0935","authenticated-orcid":false,"given":"Rahul","family":"Shukla","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Applied Mathematics, Kingsway Campus, University of Johannesburg, Auckland Park 2006, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, de Bilbao, Barrio Sarriena, 48940 Bizkaia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1073\/pnas.53.6.1272","article-title":"Fixed-point theorems for noncompact mappings in Hilbert space","volume":"53","author":"Browder","year":"1965","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1002\/mana.19650300312","article-title":"Zum Prinzip der kontraktiven Abbildung","volume":"30","year":"1965","journal-title":"Math. Nachr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.2307\/2313345","article-title":"A fixed point theorem for mappings which do not increase distances","volume":"72","author":"Kirk","year":"1965","journal-title":"Am. Math. Mon."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4387","DOI":"10.1016\/j.na.2011.03.057","article-title":"Fixed point theorem for \u03b1-nonexpansive mappings in Banach spaces","volume":"74","author":"Aoyama","year":"2011","journal-title":"Nonlinear Anal."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.jmaa.2010.08.069","article-title":"Fixed point theory for a class of generalized nonexpansive mappings","volume":"375","author":"Suzuki","year":"2011","journal-title":"J. Math. Anal. Appl."},{"key":"ref_6","unstructured":"Goebel, K., and Pineda, M.J. (2007, January 16\u201322). A new type of nonexpansiveness. Proceedings of the 8-th International Conference on Fixed Point Theory and Applications, Chiang Mai, Thailand."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1090\/S0002-9939-1972-0298500-3","article-title":"A fixed point theorem for asymptotically nonexpansive mappings","volume":"35","author":"Goebel","year":"1972","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1090\/S0002-9939-1973-0313896-2","article-title":"Fixed point theorems in reflexive Banach spaces","volume":"38","author":"Kannan","year":"1973","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4706","DOI":"10.1016\/j.na.2007.11.023","article-title":"Asymptotic pointwise contractions","volume":"69","author":"Kirk","year":"2008","journal-title":"Nonlinear Anal."},{"key":"ref_10","first-page":"1","article-title":"The fixed point theory for some generalized nonexpansive mappings","volume":"2011","year":"2011","journal-title":"Abstr. Appl. Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2010\/458265","article-title":"Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits","volume":"2010","author":"Nicolae","year":"2009","journal-title":"Fixed Point Theory Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00025-018-0930-6","article-title":"Approximating fixed points of a general class of nonexpansive mappings in Banach spaces with applications","volume":"74","author":"Pandey","year":"2019","journal-title":"Results Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1080\/01630563.2016.1276075","article-title":"Approximating fixed points of generalized \u03b1-nonexpansive mappings in Banach spaces","volume":"38","author":"Pant","year":"2017","journal-title":"Numer. Funct. Anal. Optim."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1016\/j.jmaa.2007.09.023","article-title":"Fixed point theorems and convergence theorems for some generalized nonexpansive mappings","volume":"340","author":"Suzuki","year":"2008","journal-title":"J. Math. Anal. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11784-019-0717-8","article-title":"Some fixed point results for generalized contractions of Suzuki type in Banach spaces","volume":"21","author":"Atailia","year":"2019","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"201","DOI":"10.4153\/CMB-1973-036-0","article-title":"A generalization of a fixed point theorem of Reich","volume":"16","author":"Hardy","year":"1973","journal-title":"Can. Math. Bull."},{"key":"ref_17","first-page":"103","article-title":"Asymptotic behavior of iterates of nonexpansive mappings in Banach spaces with Opial\u2019s condition","volume":"94","author":"Emmanuele","year":"1985","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"35","DOI":"10.2969\/jmsj\/03410035","article-title":"Nonlinear ergodic theorems and weak convergence theorems","volume":"34","author":"Hirano","year":"1982","journal-title":"J. Math. Soc. Jpn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1007\/s11784-018-0483-z","article-title":"Successive approximations for common fixed points of a family of \u03b1-nonexpansive mappings","volume":"20","author":"Song","year":"2018","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kirk, W.A., and Sims, B. (2013). Handbook of Metric Fixed Point Theory, Springer Science & Business Media.","DOI":"10.1186\/1687-1812-2013-106"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Chidume, C. (2009). Geometric Properties of Banach Spaces and Nonlinear Iterations, Lecture Notes in Mathematics, Springer.","DOI":"10.1007\/978-1-84882-190-3"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1090\/S0002-9904-1967-11761-0","article-title":"Weak convergence of the sequence of successive approximations for nonexpansive mappings","volume":"73","author":"Opial","year":"1967","journal-title":"Bull. Am. Math. Soc."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Cegielski, A. (2012). Iterative Methods for Fixed Point Problems in Hilbert Spaces, Lecture Notes in Mathematics, Springer.","DOI":"10.1007\/978-3-642-30901-4"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1090\/S0002-9904-1966-11544-6","article-title":"The solution by iteration of nonlinear functional equations in Banach spaces","volume":"72","author":"Browder","year":"1966","journal-title":"Bull. Am. Math. Soc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1017\/S0004972700020621","article-title":"Construction of sunny nonexpansive retractions in Banach spaces","volume":"66","author":"Benavides","year":"2002","journal-title":"Bull. Aust. Math. Soc."},{"key":"ref_26","first-page":"75","article-title":"Quelques propri\u00e9t\u00e9s de convergence asymptotique pour les semi-groupes de contractions impaires","volume":"283","author":"Baillon","year":"1976","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A-B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02760397","article-title":"On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak \u03c9-limit set","volume":"29","author":"Bruck","year":"1978","journal-title":"Isr. J. Math."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/0022-1236(78)90010-1","article-title":"On the asymptotic behavior of semigroups of nonlinear contractions in Hilbert space","volume":"27","author":"Pazy","year":"1978","journal-title":"J. Funct. Anal."},{"key":"ref_29","first-page":"212","article-title":"Asymptotic behavior of iterates of nonexpansive mappings in Banach spaces","volume":"54","author":"Miyadera","year":"1978","journal-title":"Proc. Jpn. Acad. Ser. A Math. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/0022-247X(76)90111-6","article-title":"Asymptotic behavior of semigroups of nonlinear contractions in Banach spaces","volume":"53","author":"Reich","year":"1976","journal-title":"J. Math. Anal. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1090\/S0002-9904-1967-11864-0","article-title":"Fixed points of nonexpanding maps","volume":"73","author":"Halpern","year":"1967","journal-title":"Bull. Am. Math. 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