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Because of difficulty of using Schauder’s fixed point theorem to the polynomial-like iterative equation, a lots of work are contributed to the existence of solutions for the polynomial-like iterative equation on compact set. In this paper, by applying the Schauder-Tychonoff fixed point theorem we discuss monotone solutions and convex solutions of the polynomial-like iterative equation on an open set (possibly unbounded) in RN. More concretely, by considering a partial order in RN defined by an order cone, we prove the existence of increasing and decreasing solutions of the polynomial-like iterative equation on an open set and further obtain the conditions under which the solutions are convex in the order.
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참고문헌 (29)
참고문헌 신청
A. Mukherjea / 1983 / On a functional equation involving iterates of a bijection on the unit interval / Nonlinear Anal 7 (8) : 899 ~ 908
A. Mukherjea / 1998 / A functional equation involving iterates of a bijection on the unit interval. II / Nonlinear Anal 31 (3-4) : 459 ~ 464
B. Xu / 2007 / Decreasing solutions and convex solutions of the polynomial-like iterative equation / J. Math. Anal. Appl 329 (1) : 483 ~ 497
D. Yang / 2004 / Characteristic solutions of polynomial-like iterative equations / Aequationes Math 67 (1-2) : 80 ~ 105
E. Zeidler / 1986 / Nonlinear Functional Analysis and Its Applications / Springer-Verlag
A. Mukherjea / 1998 / A functional equation involving iterates of a bijection on the unit interval. II / Nonlinear Anal 31 (3-4) : 459 ~ 464
B. Xu / 2007 / Decreasing solutions and convex solutions of the polynomial-like iterative equation / J. Math. Anal. Appl 329 (1) : 483 ~ 497
D. Yang / 2004 / Characteristic solutions of polynomial-like iterative equations / Aequationes Math 67 (1-2) : 80 ~ 105
E. Zeidler / 1986 / Nonlinear Functional Analysis and Its Applications / Springer-Verlag
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