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

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

Abstract metric spaces and Sehgal–Guseman-type theorems

AbstractRecently, 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 Radenović and Kadelburg [S. Radenović, 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

Statistics in engineering education

U ovom radu je prikazan subjektivni pristup i istraživanje obrazovanja statističkih metoda na mašinskim fakultetima zemalja Evropske unije, kao osnova za postizanje svetskog nivoa kvaliteta i konkurentnosti proizvoda i usluga na svetskom tržištu. Sugestije za poboljšanje statističkog obrazovanja su prikazane sa ciljem da se prevaziđe postojeći jaz između inženjera i naučnika koji se bave primenjenom naukom, sa jedne strane i matematičara sa druge.This paper presents a subjective view and a research of the education of the statistical methods in Mechanical Engineering Faculties in EU countries, as a base for achieving world class quality in good and services. Suggestions for an improvement of the statistical education were presented in order to overcome the existing gap between engineers and scientists on one side and mathematicians on the other

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 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

The role of NATO naval and air forces in the Mediterranean after the Cold War

Промене у међународним односима настале после Хладног рата утицале су на повећану употребу поморских и ваздухопловних снага у односу на копнене снаге у војним интервенцијама и реакцијама на кризе или појаву претњи. Поморска и ваздушна моћ су у међународним односима све више после Хладног рата почеле да се испољавају у војним интервенцијама. Употреба поморске моћи је све учесталија и више од 80 одсто интервенција и локалних ратова је вођено са мора и преко мора. Предмет истраживања представља утврђивање улоге коју поморске и ваздухопловне снаге НАТО остварују у Средоземљу после Хладног рата. Тема до сада није била предмет истраживања и у довољној мери не постоје сазнања о предмету истраживања у домаћој, али ни у иностраној стручној и научној литератури. У раду се пошло од претпоставке да је НАТО после Хладног рата све чешће користио поморске и ваздухопловне снаге за остварење дугорочних стратегијских интереса...Changes in international relations after the Cold War resulted in the increased use of naval and air forces in comparision to ground forces in military interventions, as well as responses to crises or the occurrence of threats. Therefore, naval and air power in international relations were more relevant for military interventions after the Cold War. It is particularly relevant for the use of naval power, as more than 80 percent of interventions and local wars were conducted from the sea and over the sea. The subject of research is to determine the role of the NATO naval and air forces in the Mediterranean Sea after the Cold War. This topic has not been the subject of numerous academic research and sufficient knowledge in national, nor foreign scientific literature. The dissertation is based on the assumption that NATO after the Cold War increasingly used naval and air forces to achieve long-term strategic interests..

Statistics in engineering education

U ovom radu je prikazan subjektivni pristup i istraživanje obrazovanja statističkih metoda na mašinskim fakultetima zemalja Evropske unije, kao osnova za postizanje svetskog nivoa kvaliteta i konkurentnosti proizvoda i usluga na svetskom tržištu. Sugestije za poboljšanje statističkog obrazovanja su prikazane sa ciljem da se prevaziđe postojeći jaz između inženjera i naučnika koji se bave primenjenom naukom, sa jedne strane i matematičara sa druge.This paper presents a subjective view and a research of the education of the statistical methods in Mechanical Engineering Faculties in EU countries, as a base for achieving world class quality in good and services. Suggestions for an improvement of the statistical education were presented in order to overcome the existing gap between engineers and scientists on one side and mathematicians on the other

Political and strategic changes in the Mediterranean

The paper elaborates on the geostrategic significance of the Mediterranean and the Mediterranean Sea in the past, as a precondition for consideration of current and future events in this macro-region. The author firstly considers the manifestation of the power, influence and interests of the great powers in the Mediterranean through a historical and spatial perspective. The paper analyses political and economic changes in the Mediterranean through the theoretical and practical approach of great powers` navies engagement. The author points out that the geopolitical and geostrategic importance of the Mediterranean will further increase in the future, as a result of constant regional and global aspirations to increase the political and economic dynamics of this region. The growing competition between the United States and China will have a direct impact on the Mediterranean. The author concludes that the Mediterranean will remain a „testing polygon“ for the United States, China and Russia, and a region in which political and economic processes and strategic changes in the world could be witnessed most obviously

The contraction principle for set valued mappings on a metric space with a graph

Let (X, d) be a metric space and F : X hooked right arrow X be a set valued mapping. We obtain sufficient conditions for the existence of a fixed point of the mapping F in the metric space X endowed with a graph G such that the set V(G) of vertices of G coincides with X and the set of edges of G is E(G) = {(x, y) : (x, y) is an element of X x X}