Some properties of short exact sequences of locally convex Riesz spaces

summary:We investigate the stability of some properties of locally convex Riesz spaces in connection with subspaces and quotients and also the corresponding three-space-problems. We show that in the richer structure there are more positive answers than in the category of locally convex spaces

Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones

Abstract metric spaces and Hardy-Rogers-type theorems

The purpose of the present paper is to establish coincidence point theorem for two mappings and fixed point theorem for one mapping in abstract metric space which satisfy contractive conditions of Hardy-Rogers type. Our results generalize fixed point theorems of Nemytzki [V.V. Nemytzki, Fixed point method in analysis, Uspekhi Mat. Nauk 1 (1936) 141-174], Edelstein I M. Edelstein, On fixed and periodic point under contractive mappings, J. Lond. Math. Soc. 37 (1962) 74-79] and Huang, Zhang [LG. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2)(2007) 1468-1476] from abstract metric spaces to symmetric spaces (Theorem 2.1) and to metric spaces (Theorem 2.4, Corollaries 2.6-2.8). Two examples are given to illustrate the usability of our results

Variations in the Tensorial Trapezoid Type Inequalities for Convex Functions of Self-Adjoint Operators in Hilbert Spaces

In this paper, various tensorial inequalities of trapezoid type were obtained. Identity from classical analysis is utilized to obtain the tensorial version of the said identity which in turn allowed us to obtain tensorial inequalities in Hilbert space. The continuous functions of self-adjoint operators in Hilbert spaces have several tensorial norm inequalities discovered in this study. The convexity features of the mapping f lead to the variation in several inequalities of the trapezoid type

Abstract metric spaces and Sehgal-Guseman-type theorems

Recently, Raja and Vaezpour [P. Raja and S.M. Vaezpour, Some extensions of Banach's contraction principle in complete cone metric spaces, Fixed Point Theory Appl. 2008, 11 pages, doi:10.1155/2008/768294. Article ID 768294] proved some results for Sehgal-Guseman-type theorems in the framework of abstract (cone) metric spaces over a normal solid cone. The purpose of this paper is to present this in the framework of symmetric spaces which are associated with abstract (cone) metric spaces introduced by Radenovie and Kadelburg [S. Radenovie, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, ISI J. BJMA (electronic) (in press)]. Our results extend and generalize Sehgal-Guseman-type theorems from metric and abstract metric spaces to some symmetric spaces. Examples are given to illustrate the results

Some New Observations for F-Contractions in Vector-Valued Metric Spaces of Perov's Type

The main purpose of this article is to improve, generalize and complement some recently established results for Perov's type F-contractions. In our approach, we use only the property (F1) of Wardowski while other authors employed all three conditions. Working only with the fact that the function F is strictly increasing on (0, +infinity)(m), we obtain as a consequence new families of contractive conditions in the realm of vector-valued metric spaces of Perov's type. At the end of the article, we present an example that supports obtained theoretical results and genuinely generalizes several known results in existing literature

Some fixed point results via R-functions

n/

Some New Observations for F-Contractions in Vector-Valued Metric Spaces of Perov's Type

The main purpose of this article is to improve, generalize and complement some recently established results for Perov's type F-contractions. In our approach, we use only the property (F1) of Wardowski while other authors employed all three conditions. Working only with the fact that the function F is strictly increasing on (0, +infinity)(m), we obtain as a consequence new families of contractive conditions in the realm of vector-valued metric spaces of Perov's type. At the end of the article, we present an example that supports obtained theoretical results and genuinely generalizes several known results in existing literature