{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T09:46:49Z","timestamp":1726048009370},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2020,10,23]],"date-time":"2020-10-23T00:00:00Z","timestamp":1603411200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,23]],"date-time":"2020-10-23T00:00:00Z","timestamp":1603411200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s12190-020-01445-1","type":"journal-article","created":{"date-parts":[[2020,10,23]],"date-time":"2020-10-23T07:02:47Z","timestamp":1603436567000},"page":"507-525","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Approximation of fixed point and its application to fractional differential equation"],"prefix":"10.1007","volume":"66","author":[{"given":"Sabiya","family":"Khatoon","sequence":"first","affiliation":[]},{"given":"Izhar","family":"Uddin","sequence":"additional","affiliation":[]},{"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,23]]},"reference":[{"key":"1445_CR1","first-page":"223","volume":"66","author":"M Abbas","year":"2014","unstructured":"Abbas, M., Nazir, T.: A new faster iteration process applied to constrained minimization and feasibility problems. Matematicki Vesnik. 66, 223\u2013234 (2014)","journal-title":"Matematicki Vesnik."},{"key":"1445_CR2","first-page":"61","volume":"8","author":"RP Agarwal","year":"2007","unstructured":"Agarwal, R.P., O\u2019Regan, D., Sahu, D.R.: Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex A. 8, 61\u201379 (2007)","journal-title":"J. Nonlinear Convex A."},{"key":"1445_CR3","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.amc.2014.10.082","volume":"257","author":"R Agarwal","year":"2015","unstructured":"Agarwal, R., Baleanu, D., Hedayati, V., Rezapour, S.: Two fractional derivative inclusion problems via integral boundary condition. Appl. Math. Comput. 257, 205\u2013212 (2015)","journal-title":"Appl. Math. Comput."},{"issue":"9","key":"1445_CR4","first-page":"2151","volume":"21","author":"J Ali","year":"2020","unstructured":"Ali, J., Ali, F.: A new iterative scheme to approximating fixed points of and the solution of a delay differential equation. J. Nonlinear Convex Anal. 21(9), 2151\u20132163 (2020)","journal-title":"J. Nonlinear Convex Anal."},{"key":"1445_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/s00366-020-01172-y","author":"J Ali","year":"2020","unstructured":"Ali, J., Jubair, M., Ali, F.: Stability and convergence of F iterative scheme with an application to the fractional differential equation. Eng. Comput. (2020). https:\/\/doi.org\/10.1007\/s00366-020-01172-y","journal-title":"Eng. Comput."},{"issue":"6","key":"1445_CR6","doi-asserted-by":"publisher","first-page":"522","DOI":"10.3390\/math7060522","volume":"7","author":"J Ali","year":"2019","unstructured":"Ali, J., Ali, F., Kumar, P.: Approximation of fixed points for Suzuki\u2019s generalized non-expansive mappings. Mathematics. 7(6), 522 (2019)","journal-title":"Mathematics."},{"issue":"13","key":"1445_CR7","doi-asserted-by":"crossref","first-page":"4387","DOI":"10.1016\/j.na.2011.03.057","volume":"74","author":"K Aoyama","year":"2011","unstructured":"Aoyama, K., Kohsaka, F.: Fixed point theorem for $$\\alpha $$-nonexpansive mappings in Banach spaces. Nonlinear Anal. 74(13), 4387\u20134391 (2011)","journal-title":"Nonlinear Anal."},{"key":"1445_CR8","first-page":"2013","volume":"371","author":"D Baleanu","year":"1990","unstructured":"Baleanu, D., Rezapour, S., Mohammadi, H.: Some existence results on nonlinear fractional differential equations. Philos. Trans. R Soc. A Math. Phys. Eng. Sci. 371, 2013 (1990)","journal-title":"Philos. Trans. R Soc. A Math. Phys. Eng. Sci."},{"key":"1445_CR9","doi-asserted-by":"publisher","first-page":"1272","DOI":"10.1073\/pnas.53.6.1272","volume":"53","author":"FE Browder","year":"1965","unstructured":"Browder, F.E.: Fixed-point theorems for noncompact mappings in Hilbert space. Proc. Natl. Acad. Sci. USA 53, 1272\u20131276 (1965)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"issue":"4","key":"1445_CR10","doi-asserted-by":"publisher","first-page":"3182","DOI":"10.3934\/math.2020205","volume":"5","author":"C Garodia","year":"2020","unstructured":"Garodia, C., Uddin, I.: A new fixed point algorithm for finding the solution of a delay differential equation. AIMS Math. 5(4), 3182\u20133200 (2020)","journal-title":"AIMS Math."},{"issue":"3","key":"1445_CR11","first-page":"986","volume":"10","author":"C Garodia","year":"2020","unstructured":"Garodia, C., Uddin, I.: A new iterative method for solving split feasibility problem. J. Appl. Anal. Comput. 10(3), 986\u20131004 (2020)","journal-title":"J. Appl. Anal. Comput."},{"key":"1445_CR12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511526152","volume-title":"Topic in Metric Fixed Point Theory","author":"K Geobel","year":"1990","unstructured":"Geobel, K., Kirk, W.A.: Topic in Metric Fixed Point Theory. Cambridge University Press, Cambridge (1990)"},{"key":"1445_CR13","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1002\/mana.19650300312","volume":"30","author":"D G\u00f6hde","year":"1965","unstructured":"G\u00f6hde, D.: Zum Prinzip def Kontraktiven Abbilding. Math. Nachr. 30, 251\u2013258 (1965)","journal-title":"Math. Nachr."},{"issue":"1","key":"1445_CR14","first-page":"193","volume":"17","author":"M Gregu\u0161 Jr","year":"1980","unstructured":"Gregu\u0161 Jr., M.: A fixed point theorem in Banach space. Boll. Univ. Math. Italy A 17(1), 193\u2013198 (1980)","journal-title":"Boll. Univ. Math. Italy A"},{"issue":"10","key":"1445_CR15","doi-asserted-by":"publisher","first-page":"2829","DOI":"10.2298\/FIL1610829G","volume":"30","author":"F G\u00fcrsoy","year":"2016","unstructured":"G\u00fcrsoy, F.: A Picard-S iterative method for approximating fixed point of weak-contraction mappings. Filomat 30(10), 2829\u20132845 (2016)","journal-title":"Filomat"},{"issue":"16","key":"1445_CR16","doi-asserted-by":"publisher","first-page":"7393","DOI":"10.1007\/s00500-018-3384-6","volume":"23","author":"F G\u00fcrsoy","year":"2019","unstructured":"G\u00fcrsoy, F., Eksteen, J.J.A., Khan, A.R., Karakaya, V.: An iterative method and its application to stable inversion. Soft Comput. 23(16), 7393\u20137406 (2019)","journal-title":"Soft Comput."},{"key":"1445_CR17","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1080\/01630563.2017.1363774","volume":"39","author":"F G\u00fcrsoy","year":"2018","unstructured":"G\u00fcrsoy, F., Khan, A.R., Ert\u00fcrk, M., Karakaya, V.: Convergence and data dependency of normal-S iterative method for discontinuous operators on Banach space. Numer. Funct. Anal. Optim. 39, 322\u2013345 (2018)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"1445_CR18","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1090\/S0002-9904-1967-11864-0","volume":"73","author":"B Halpern","year":"1967","unstructured":"Halpern, B.: Fixed points of nonexpanding maps. B Am. Math. Soc. 73, 957\u2013961 (1967)","journal-title":"B Am. Math. Soc."},{"issue":"1","key":"1445_CR19","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1090\/S0002-9939-1974-0336469-5","volume":"44","author":"S Ishikawa","year":"1974","unstructured":"Ishikawa, S.: Fixed points by a new iteration method. Proc. Am. Math. Soc. 44(1), 147\u2013150 (1974)","journal-title":"Proc. Am. Math. Soc."},{"issue":"1","key":"1445_CR20","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1090\/S0002-9939-1973-0313896-2","volume":"38","author":"R Kannan","year":"1973","unstructured":"Kannan, R.: Fixed point theorems in reflexive Banach spaces. Proc. Am. Math. Soc. 38(1), 111\u2013118 (1973)","journal-title":"Proc. Am. Math. Soc."},{"key":"1445_CR21","first-page":"1","volume":"421","author":"E Karapnar","year":"2019","unstructured":"Karapnar, E., Abdeljawa, T., Jarad, F.: Applying new fixed point theorems on fractional and ordinary differential equations. Adv. Differ. Eq. 421, 1\u201325 (2019)","journal-title":"Adv. Differ. Eq."},{"key":"1445_CR22","doi-asserted-by":"publisher","first-page":"1004","DOI":"10.2307\/2313345","volume":"72","author":"WA Kirk","year":"1965","unstructured":"Kirk, W.A.: A fixed point theorem for mappings which do not increase distances. Am. Math. Mon. 72, 1004\u20131006 (1965)","journal-title":"Am. Math. Mon."},{"key":"1445_CR23","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1090\/S0002-9939-1953-0054846-3","volume":"4","author":"WR Mann","year":"1953","unstructured":"Mann, W.R.: Mean value methods in iteration. Proc. Am. Math. Soc. 4, 506\u2013510 (1953)","journal-title":"Proc. Am. Math. Soc."},{"key":"1445_CR24","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1006\/jmaa.2000.7042","volume":"251","author":"MA Noor","year":"2000","unstructured":"Noor, M.A.: New approximation schemes for general variational inequalities. J. Math. Anal. Appl. 251, 217\u2013229 (2000)","journal-title":"J. Math. Anal. Appl."},{"issue":"4","key":"1445_CR25","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1090\/S0002-9904-1967-11761-0","volume":"73","author":"Z Opial","year":"1967","unstructured":"Opial, Z.: Weak convergence of the sequence of successive approximations for non-expansive mappings. Bull. Am. Math. Soc. 73(4), 595\u2013597 (1967)","journal-title":"Bull. Am. Math. Soc."},{"key":"1445_CR26","doi-asserted-by":"crossref","unstructured":"Pandey, R., Pant, R., Rako\u010devi\u010d, V., Shukla, R.,: Approximating fixed points of a general class of nonexpansive mappings in Banach spaces with applications. Results Math. 74(1), Article No. 7 (2019)","DOI":"10.1007\/s00025-018-0930-6"},{"issue":"1","key":"1445_CR27","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1017\/S0004972700028884","volume":"43","author":"J Schu","year":"1991","unstructured":"Schu, J.: Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Bull. Austral. Math. Soc. 43(1), 153\u2013159 (1991)","journal-title":"Bull. Austral. Math. Soc."},{"key":"1445_CR28","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1090\/S0002-9939-1974-0346608-8","volume":"44","author":"HF Senter","year":"1974","unstructured":"Senter, H.F., Dotson, W.G.: Approximating fixed points of nonexpansive mappings. Proc. Am. Math. Soc. 44, 375\u2013380 (1974)","journal-title":"Proc. Am. Math. Soc."},{"issue":"2","key":"1445_CR29","doi-asserted-by":"publisher","first-page":"1088","DOI":"10.1016\/j.jmaa.2007.09.023","volume":"340","author":"T Suzuki","year":"2008","unstructured":"Suzuki, T.: Fixed point theorems and convergence theorems for some generalized nonexpansive mappings. J. Math. Anal. Appl. 340(2), 1088\u20131095 (2008)","journal-title":"J. Math. Anal. Appl."},{"key":"1445_CR30","doi-asserted-by":"publisher","first-page":"2711","DOI":"10.2298\/FIL1610711T","volume":"30","author":"D Thakur","year":"2016","unstructured":"Thakur, D., Thakur, B.S., Postolache, M.: A new iteration scheme for approximating fixed points of nonexpansive mappings. Filomat 30, 2711\u20132720 (2016)","journal-title":"Filomat"},{"key":"1445_CR31","doi-asserted-by":"publisher","first-page":"187","DOI":"10.2298\/FIL1801187U","volume":"32","author":"K Ullah","year":"2018","unstructured":"Ullah, K., Arshad, M.: Numerical reckoning fixed points for Suzuki\u2019s generalized nonexpansive mappings via new iteration process. Filomat 32, 187\u2013196 (2018)","journal-title":"Filomat"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01445-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-020-01445-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01445-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T23:23:23Z","timestamp":1698276203000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-020-01445-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,23]]},"references-count":31,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1445"],"URL":"https:\/\/doi.org\/10.1007\/s12190-020-01445-1","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,23]]},"assertion":[{"value":"3 August 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 October 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 October 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}