Existence and Iterative Approximations of Solutions for Certain Functional Equation and Inequality

Autor:	Zeqing Liu, Haijiang Dong, Sun Young Cho, Shin Min Kang
Rok vydání:	2012
Předmět:	Control and Optimization Approximations of π Applied Mathematics Mathematical analysis Banach space Management Science and Operations Research Complete metric space Dynamic programming Bounded function Functional equation Theory of computation Applied mathematics Uniqueness Mathematics
Zdroj:	Journal of Optimization Theory and Applications. 157:716-736
ISSN:	1573-2878 0022-3239
DOI:	10.1007/s10957-012-0185-4
Popis:	This paper deals with a functional equation and inequality arising in dynamic programming of multistage decision processes. Using several fixed-point theorems due to Krasnoselskii, Boyd–Wong and Liu, we prove the existence and/or uniqueness and iterative approximations of solutions, bounded solutions and bounded continuous solutions for the functional equation in two Banach spaces and a complete metric space, respectively. Utilizing the monotone iterative method, we establish the existence and iterative approximations of solutions and nonpositive solutions for the functional inequality in a complete metric space. Six examples which dwell upon the importance of our results are also included.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::248ab6169402e9551849340f0591454e https://doi.org/10.1007/s10957-012-0185-4 Zobrazit plný text záznamu Full text from SpringerLink