Now showing items 1-8 of 8

    • Fixed Point Theorems on Closed Sets Through Abstract Cones 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1976-03)
      **Please note that the full text is embargoed** ABSTRACT: Let D be a closed subset of a complete metric space (X,p). We seek (i) conditions upon which a map T : D -> X has a fixed point in D and (ii) the construction of ...
    • Fixed Point Theorems Through Abstract Cones 

      Eisenfeld, Jerome; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-03)
      **Please note that the full text is embargoed** ABSTRACT: A well-known theorem of Banach states that if T is a mapping on a complete metric space [see pdf for notation] such that for some number [see pdf for notation], the ...
    • Maximal and Minimal Solutions and Comparison Principle for Differential Equations in Abstract Cones 

      Mitchell, Roger W.; Mitchell, A. Richard; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)
      **Please note that the full text is embargoed** ABSTRACT: Existence of maximal and minimal solutions for differential equations in abstract cones is established without requiring uniform continuity. Utilizing such a result ...
    • Method of Quasi-Upper and Lower Solutions in Abstract Cones 

      Lakshmikantham, V.; Vatsala, A. S.; Leela, S. (University of Texas at ArlingtonDepartment of Mathematics, 1981-05)
      **Please note that the full text is embargoed** ABSTRACT: Let E be a real Banach space with ||•|| and let E* denote the dual of E. Let K C E be a cone, that is, a closed convex subset such that ^K C K for every ^ ≥ 0 and ...
    • The Method of Quasilinearization and Positivity of Solutions in Abstract Cones 

      Lakshmikantham, V.; Sety, Dolores D.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1976-03)
      **Please note that the full text is embargoed** ABSTRACT: The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the ...
    • Monotone Iterative Technique for Differential Equations in a Banach Space 

      Lakshmikantham, V.; Du, Sen-Wo (University of Texas at ArlingtonDepartment of Mathematics, 1981-02)
      **Please note that the full text is embargoed** ABSTRACT: Let E be a real Banach space with norm [see pdf for notation]. Consider the initial value problem (1.1) [see pdf for notation], where [see pdf for notation]. ...
    • On the Method of Upper and Lower Solutions in Abstract Cones 

      Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1981-02)
      **Please note that the full text is embargoed**
    • Remarks on Nonlinear Contraction and Comparison Principle in Abstract Cones 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)
      **Please note that the full text is embargoed** ABSTRACT: The contraction mapping principle and the Schauder principle can both be viewed as a comparison of maps. For the former one has a condition of the type [see pdf for ...