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)
      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 an iterative sequence whose limit is a fixed point in D. ...
    • Fixed Point Theorems Through Abstract Cones 

      Eisenfeld, Jerome; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-03)
      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 inequality (1.1) [see pdf for notation] holds, then T has ...
    • 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)
      Existence of maximal and minimal solutions for differential equations in abstract cones is established without requiring uniform continuity. Utilizing such a result an abstract comparison principle is developed. The results ...
    • 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)
      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 K ^ {-K} = {O}, By means of K a partial order ≤ is defined ...
    • 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)
      The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the method can be found in (Ref. 3). This method has been very ...
    • Monotone Iterative Technique for Differential Equations in a Banach Space 

      Lakshmikantham, V.; Du, Sen-Wo (University of Texas at ArlingtonDepartment of Mathematics, 1981-02)
      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]. Generally speaking of approximate solutions of (1.1) consist ...
    • On the Method of Upper and Lower Solutions in Abstract Cones 

      Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1981-02)
    • Remarks on Nonlinear Contraction and Comparison Principle in Abstract Cones 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)
      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 notation] and for the latter one has a condition of the ...