• Title/Summary/Keyword: system of functional equations

Search Result 8, Processing Time 0.111 seconds

COMMON FIXED POINTS FOR COMPATIBLE MAPPINGS OF TYPE (P) AND AN APPLICATION IN DYNAMIC PROGRAMMING

  • Liu, Zeqing;Guo, Zhenyu;Kang, Shin-Min;Shim, Soo-Hak
    • Journal of applied mathematics & informatics
    • /
    • v.26 no.1_2
    • /
    • pp.61-73
    • /
    • 2008
  • In this paper common fixed point theorems dealing with compatible mappings of type (P) are established. As a application, the existence and uniqueness of common solution for a system of functional equations arising in dynamic programming is given. The results presented in this paper improve, generalize and unify the corresponding results in this field.

  • PDF

COMMON FIXED POINT THEOREMS FOR COMPATIBLE MAPPINGS OF TYPE (A) AND (P) WITH APPLICATIONS IN DYNAMIC PROGRAMMING

  • Jiang, Guojing;Liu, Min;Lee, Suk-Jin;Kang, Shin-Min
    • East Asian mathematical journal
    • /
    • v.25 no.1
    • /
    • pp.11-26
    • /
    • 2009
  • In this paper, the concepts of compatible mappings of types (A) and (P) are introduced in an induced metric space, two common xed point theorems for two pairs of compatible mappings of types (A) and (P) in an induced complete metric space are established. As their applications, the existence and uniqueness results of common solution for a system of functional equations arising in dynamic programming are discussed.

  • PDF

COMMON FIXED POINT THEOREMS FOR CONTRACTIVE TYPE MAPPINGS AND THEIR APPLICATIONS IN DYNAMIC PROGRAMMING

  • Liu, Zeqing;Wang, Lili;Kim, Hyeong-Kug;Kang, Shin-Min
    • Bulletin of the Korean Mathematical Society
    • /
    • v.45 no.3
    • /
    • pp.573-585
    • /
    • 2008
  • A few sufficient conditions for the existence and uniqueness of fixed point and common fixed point for certain contractive type mappings in complete metric spaces are provided. Several existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in dynamic programming are discussed by using the fixed point and common fixed point theorems presented in this paper.

A General System of Nonlinear Functional Equations in Non-Archimedean Spaces

  • Ghaemi, Mohammad Bagher;Majani, Hamid;Gordji, Madjid Eshaghi
    • Kyungpook Mathematical Journal
    • /
    • v.53 no.3
    • /
    • pp.419-433
    • /
    • 2013
  • In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.

COMMON FIXED POINT THEOREMS WITH APPLICATIONS TO THE SOLUTIONS OF FUNCTIONAL EQUATIONS ARISING IN DYNAMIC PROGRAMMING

  • Liu, Zeqing;Liu, Min;Kim, Hyeong-Kug;Kang, Shin-Min
    • Communications of the Korean Mathematical Society
    • /
    • v.24 no.1
    • /
    • pp.67-83
    • /
    • 2009
  • Several common fixed point theorems for a few contractive type mappings in complete metric spaces are established. As applications, the existence and uniqueness of common solutions for certain systems of functional equations arising in dynamic programming are discussed.

SOME FIXED POINT THEOREMS VIA COMMON LIMIT RANGE PROPERTY IN NON-ARCHIMEDEAN MENGER PROBABILISTIC METRIC SPACES

  • Nashine, Hemant Kumar;Kadelburg, Zoran
    • Bulletin of the Korean Mathematical Society
    • /
    • v.52 no.3
    • /
    • pp.789-807
    • /
    • 2015
  • We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.