{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T16:00:34Z","timestamp":1768147234503,"version":"3.49.0"},"reference-count":16,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Department of Science and Technology, Government of India","award":["DST\/INSPIRE Fellowship\/2013\/[182]"],"award-info":[{"award-number":["DST\/INSPIRE Fellowship\/2013\/[182]"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>The paper deals with the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming of multistage decision making processes in Banach spaces<jats:italic>BC(S)<\/jats:italic>and<jats:italic>B(S)<\/jats:italic>and complete metric space<jats:italic>BB(S)<\/jats:italic>, respectively. Our main results extend, improve, and generalize the results due to several authors. Some examples are also given to demonstrate the advantage of our results over existing one in the literature.<\/jats:p>","DOI":"10.1155\/2014\/706585","type":"journal-article","created":{"date-parts":[[2014,4,8]],"date-time":"2014-04-08T21:54:05Z","timestamp":1396994045000},"page":"1-9","source":"Crossref","is-referenced-by-count":10,"title":["Existence Theorems for Solvability of a Functional Equation Arising in Dynamic Programming"],"prefix":"10.1155","volume":"2014","author":[{"family":"Deepmala","sequence":"first","affiliation":[{"name":"School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"2","year":"1957"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(84)90254-3"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(88)90201-6"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023945621360"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.04.049"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.04.033"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s10255-007-0363-6"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/701519"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1969-0239559-9"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.12.093"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2001.7551"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/245872"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/S0252-9602(13)60083-1"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1812-2013-196"},{"issue":"3","key":"9","first-page":"475","volume":"11","year":"2010","journal-title":"Journal of Nonlinear and Convex Analysis"},{"key":"15","volume":"2013, article 516","year":"2013","journal-title":"Journal of Inequalities and Applications"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/706585.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/706585.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/706585.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T05:48:52Z","timestamp":1469771332000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2014\/706585\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":16,"alternative-id":["706585","706585"],"URL":"https:\/\/doi.org\/10.1155\/2014\/706585","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}