$p$-Adic Approach to Linear 2-Normed Spaces
Mathematica Moravica, Vol. 13-2 (2009), 7–22.
Download PDF file: (435kB) |
Abstract. We shall construct some new $p$-adic approaches to linear 2-normed spaces by using the facts that known about $p$-adic numbers, $p$-adic analysis and give some results in this sense.
Keywords. 2-normed spaces, $p$-adic numbers, $p$-adic norm, $p$-adic 2-norm.
A Procedure for Obtaining a Family of Iterative Formulas of Higher Order
Mathematica Moravica, Vol. 13-2 (2009), 23–26.
Download PDF file: (267kB) |
Abstract. In this paper a procedure for obtaining iterative formulas of higher order for finding zeros is obtained. The family includes several already known results.
Keywords. Iteration formulas, approximate solutions of equations.
Algebras of General Convexity and General Concavity, Nonlinear Programming, Physics, and Inequalities
Mathematica Moravica, Vol. 13-2 (2009), 27–102.
Download PDF file: (600kB) |
Abstract. In this paper we introduced the fundamental elements of new algebras of general convexity and general concavity. This paper presents essential elements of a new general convex (concave) functional analysis. Applications in linear and nonlinear functional analysis, linear and nonlinear programming, physics, and inequalities are considered. Adequate to fundamental fact that every set has three own sides (upper, lower and middle) we introduced and consider three relativistic physics (general convex, general concave and middle) and three physics in the classical sense. In this context we obtain relativistic Einstein's theory as a relativistic physics on the middle transversal linear spaces.
Keywords. General convex structures, general convex spaces, algebras of general convexity and general concavity, general convex functional analysis, physics of general convexity and general concavity, Einstein's physics, nonlinear programming, principles of relativity, inequalities of transversal general convex functions.
Every Set Has at Least Three Choice Functions
Mathematica Moravica, Vol. 13-2 (2009), 103–116.
Download PDF file: (469kB) |
Abstract. This paper continues the study of the Axiom of Choice by E. Zermelo [Neuer Beweis für die Möglichkeit einer Wohlordung, Math. Annalen, 65 (1908), 107-128; translated in van Heijenoort 1967, 183-198]. We prove some new equivalents of the Axiom of Choice, i.e., Zorn's lemma, and in connection with an initial equivalent also fact that every set has at least three choice functions.
Keywords. Axiom of choice, three choice functions.
On a Result of W.A. Kirk and L.M. Saliga
Mathematica Moravica, Vol. 13-2 (2009), 117–119.
Download PDF file: (129kB) |
Abstract. We prove that a result of Kirk and Saliga [J. Comput. Appl. Math., 113 (2000), 141-152, Theorem 4.2., p. 149] has been for the first time proved before 25 years in Tasković [Publ. Inst. Math., 41 (1980), 249-258, Theorem 1, p. 250]. But the authors neglected and ignored this historical fact.
Keywords. Fixed points, diametral $\varphi$-contractions, complete metric spaces, nonlinear conditions for fixed points, optimization.