{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T15:40:52Z","timestamp":1768837252621,"version":"3.49.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,12,14]],"date-time":"2013-12-14T00:00:00Z","timestamp":1386979200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2014,11]]},"DOI":"10.1007\/s11075-013-9813-9","type":"journal-article","created":{"date-parts":[[2013,12,13]],"date-time":"2013-12-13T07:31:09Z","timestamp":1386919869000},"page":"623-636","source":"Crossref","is-referenced-by-count":23,"title":["On multiplicative and Volterra minimization methods"],"prefix":"10.1007","volume":"67","author":[{"given":"Ali","family":"\u00d6zyap\u0131c\u0131","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mustafa","family":"Riza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B\u00fclent","family":"Bilgehan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Agamirza E.","family":"Bashirov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,12,14]]},"reference":[{"issue":"1","key":"9813_CR1","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s11071-006-9156-3","volume":"50","author":"D Aniszewska","year":"2007","unstructured":"Aniszewska, D.: Multiplicative Runge\u2013Kutta methods. Nonlinear Dyn. 50(1), 265\u2013272 (2007)","journal-title":"Nonlinear Dyn."},{"issue":"3","key":"9813_CR2","doi-asserted-by":"crossref","first-page":"60","DOI":"10.29333\/ojcmt\/2339","volume":"1","author":"AE Bashirov","year":"2011","unstructured":"Bashirov, A.E., Bashirova, G.: Dynamics of literary texts and diffusion. Online J. Commun. Media Technol. 1(3), 60\u201382 (2011)","journal-title":"Online J. Commun. Media Technol."},{"issue":"1","key":"9813_CR3","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jmaa.2007.03.081","volume":"337","author":"AE Bashirov","year":"2008","unstructured":"Bashirov, A.E., Kurp\u0131nar, E.M., \u00d6zyap\u0131c\u0131, A.: Multiplicative calculus and its applications. J. Math. Anal. Appl. 337(1), 36\u201348 (2008)","journal-title":"J. Math. Anal. Appl."},{"issue":"4","key":"9813_CR4","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/s11766-011-2767-6","volume":"26","author":"AE Bashirov","year":"2011","unstructured":"Bashirov, A.E., M\u0131s\u0131rl\u0131, E., Tando\u011fdu, Y., \u00d6zyap\u0131c\u0131, A.: On modeling with multiplicative differential equations. Appl. Math. J Chin. Univ. 26(4), 425\u2013438 (2011)","journal-title":"Appl. Math. J Chin. Univ."},{"issue":"1","key":"9813_CR5","first-page":"51","volume":"1","author":"AE Bashirov","year":"2011","unstructured":"Bashirov, A.E., Riza, M.: On complex multiplicative differentiation. TWMS J. Appl. Eng. Math. 1(1), 51\u201361 (2011)","journal-title":"TWMS J. Appl. Eng. Math."},{"key":"9813_CR6","unstructured":"Bashirov, A.E., Riza, M.: On complex multiplicative integration. arXiv: 1307.8293v1 (2013)"},{"key":"9813_CR7","unstructured":"C\u00f3rdova-Lepe, F.: The multiplicative derivative as a measure of elasticity in economics. TMAT Revista Latinoamericana de Ciencias e Ingenieria 2(3) (2006)"},{"issue":"6","key":"9813_CR8","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1111\/j.1539-6924.2008.01194.x","volume":"29","author":"J Englehardt","year":"2009","unstructured":"Englehardt, J., Swartout, J., Loewenstine, C.: A new theoretical discrete growth distribution with verification for microbial counts in water. Risk Anal. 29(6), 841\u2013856 (2009)","journal-title":"Risk Anal."},{"key":"9813_CR9","unstructured":"Filip, D.A., Piatecki, C.: A non-Newtonian examination of the theory of exogenous economic growth. CNCSIS-UEFISCSU (project number PNII IDEI 2366\/2008) and Laboratoire d\u2019Economie d\u2019Orleans (LEO) (2010)"},{"issue":"1","key":"9813_CR10","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/s10851-011-0275-1","volume":"42","author":"L Florack","year":"2012","unstructured":"Florack, L., van Assen, H.: Multiplicative calculus in biomedical image analysis. J. Math. Imaging Vis. 42(1), 64\u201375 (2012)","journal-title":"J. Math. Imaging Vis."},{"key":"9813_CR11","volume-title":"Bigeometric Calculus","author":"M Grossman","year":"1983","unstructured":"Grossman, M.: Bigeometric Calculus. Archimedes Foundation, Rockport, Mass (1983)"},{"key":"9813_CR12","volume-title":"Non-Newtonian Calculus","author":"M Grossman","year":"1972","unstructured":"Grossman, M., Katz, R.: Non-Newtonian Calculus. Lee Press, Pigeon Cove, Mass (1972)"},{"issue":"738","key":"9813_CR13","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1098\/rspa.1924.0082","volume":"106","author":"JE Jones","year":"1924","unstructured":"Jones, J.E.: On the determination of molecular fields from the equation of state of a gas. Proc. R. Soc. Lond. Ser. A 106(738), 463\u2013477 (1924)","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"9813_CR14","volume-title":"Dimensions, Invariants Models and Fractals","author":"W Kasprzak","year":"2004","unstructured":"Kasprzak, W., Lysik, B., Rybaczuk, M.: Dimensions, Invariants Models and Fractals. Ukrainian Society on Fracture Mechanics, SPOLOM,Wroclaw-Lviv (2004)"},{"issue":"4","key":"9813_CR15","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/s11075-010-9437-2","volume":"57","author":"E M\u0131s\u0131rl\u0131","year":"2011","unstructured":"M\u0131s\u0131rl\u0131, E., G\u00fcrefe, Y.: Multiplicative Adams\u2013Bashforth\u2013Moulton methods. Numer. Algo. 57(4), 425\u2013439 (2011)","journal-title":"Numer. Algo."},{"issue":"2","key":"9813_CR16","first-page":"227","volume":"12","author":"E M\u0131s\u0131rl\u0131","year":"2009","unstructured":"M\u0131s\u0131rl\u0131, E., \u00d6zyap\u0131c\u0131, A.: Exponential approximations on multiplicative calculus. Proc. Jangjeon Math. Soc. 12(2), 227\u2013236 (2009)","journal-title":"Proc. Jangjeon Math. Soc."},{"issue":"4","key":"9813_CR17","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1090\/S0033-569X-09-01158-2","volume":"67","author":"M Riza","year":"2009","unstructured":"Riza, M., \u00d6zyap\u0131c\u0131, A., M\u0131s\u0131rl\u0131, E.: Multiplicative finite difference methods. Q. Appl. Math. 67(4), 745 (2009)","journal-title":"Q. Appl. Math."},{"issue":"10","key":"9813_CR18","doi-asserted-by":"crossref","first-page":"2725","DOI":"10.1016\/j.camwa.2010.08.089","volume":"60","author":"A \u00dczer","year":"2010","unstructured":"\u00dczer, A.: Multiplicative type complex calculus as an alternative to the classical calculus. Comput. Math. Appl. 60(10), 2725\u20132737 (2010)","journal-title":"Comput. Math. Appl."},{"key":"9813_CR19","volume-title":"Operations Infinitesimales Lineares","author":"V Volterra","year":"1938","unstructured":"Volterra, V., Hostinsky, B.: Operations Infinitesimales Lineares. Gauthier-Villars, Paris (1938)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-013-9813-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-013-9813-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-013-9813-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,19]],"date-time":"2022-03-19T17:09:38Z","timestamp":1647709778000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-013-9813-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,14]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,11]]}},"alternative-id":["9813"],"URL":"https:\/\/doi.org\/10.1007\/s11075-013-9813-9","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,14]]}}}