BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

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6 Niooleta Negoescu Observation 8. Si μ ne satisfant pas à l’inégalité (2) de la Definition 3 ( μ n’est pas symétrique) alors μ est une pseudo-quasimétrique (Hicks, 1988). Les Theorems 1, 2, 3 sont vrais aussi dans ce cas, mais nous ne pouvons plus démontrer l’unicité du point fixe. BIBLIOGRAPHIE Cirić L. B., On Some Maps with Non-unique Fixed Point. Publ. Inst. Math., 17(34), 52- 58 (1974). Engelking R., Outline of General Topology. Amsterdam–Warszawa, 1998. Fisher B., Fixed Points and Constant Mappings on Metric Spaces. Rend. Acad. Lincei, 61, 129-332 (1970). Hicks T. L., Fixed Point Theorems for Quasi-metric Spaces. Math. Japonica, 33, 233- 236 (1988). Jain R. K., Dixit S. P., Some Fixed Point Theorems for Mappings in Pseudocompact Tihonov Spaces. Bull. Math., Debrecen, 33, 195-197 (1986). Lab S. N., Das M., Mappings with Common Invariant Points in 2-Metric Spaces (I and II), Math. Sem. Notes, Kobe, 8, 83-90 (1980) and 10, 691-695 (1982).. Negoescu Nicoleta, Extensions des théorèmes de R. K. Jain et S. P. Dixit. Vol. Itinerant Seminar of Functional Equations, Approximation and Convexity, Univ. Cluj- Napoca, 1988, pp. 243-248. Negoescu Nicoleta, Un théorème de point fixe pour deux applications commutatives d’un certain type de contractivité. Studii şi cercetări ştiinţifice, Univ. Bacău, Ser. Matematica, 2, 85-86 (1992). Taniguchi T., Common Fixed Point Theorems on Extension Type Mappings on Complete Metric Spaces. Math. Japonica, 34, 139-142 (1989). REZULTATE DE PUNCT FIX PENTRU OPERATORI ŞI ŞIRURI DE OPERATORI CONTRACTIVI PE SPAŢII PSEUDOCOMPACTE (Rezumat) Se demonstrează trei teoreme de punct fix pentru operatori şi şiruri de operatori care satisfac inegalităţi contractive (1), (1’), (1’’) definiţi pe spaţii metrice pseudocompacte.
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi Tomul LVIII (LXII), Fasc. 3, 2012 Secţia MATEMATICĂ. MECANICĂ TEORETICĂ. FIZICĂ ON SOME AXIAL-SYMMETRIC PROBLEMS OF THE MICROPOLAR ELASTICITY THEORY BY ION CRĂCIUN ∗ “Gheorghe Asachi” Technical University of Iaşi, Department of Mathematics and Informatics Received: May 28, 2012 Accepted for publication: July 20, 2012 Abstract. The steady vibrations of the linear theory of micropolar elasticity of an isotropic, homogeneous, and centrosymmetric elastic body occupying the three dimensional region B are considered. A generalized Galerkin representation of a regular solution of basic differential equations in B of this theory is given. In the case of cylindrical coordinates (, r θ, z) under the assumption of axially symmetry (causes and effects do not depend of the variable θ), from governing equations in the amplitudes of displacement and rotation vectors we obtain two independently systems, each one containing three partial differential equations. The unknowns of the second system are the second component of the amplitude of displacement vector u, and the first and the third components of the amplitude of rotation vector φ , all depending only of variables r and z in B, for each θ. The aim of this paper is the study of such obtained system. Thus, the Galerkin representation of a regular solution by stress functions is obtained, the actions both of body and couple-body loadings are analysed, and the action of a concentrated couple-body is considered. Key words: micropolar elasticity; axially-symmetric problems; stress functions; concentrated loadings. 1. Introduction The classical theory of elasticity is inadequate to represent the behaviour of certain materials such as polycrystalline materials, granular bodies, bodies ∗ e-mail: ialcraciun@yahoo.com
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