Volume 19, No. 1 (2009)
Articles
ON CESÁRO MEANS OF HYPERGEOMETRIC FUNCTIONS
MASLINA DARUS(*), RABHA W. IBRAHIM(**)
The polynomial approximants which retain the zero free property of a given analytic functions in the unit disk of the form (...). The convolution methods of a geometric functions that the Cesaro means of order μ retains the zero free property of the derivatives of bounded convex functions in the unit disk are used. Other properties are established.
CHARACTERIZATIONS OF FUNCTIONS WITH STRONGLY α - CLOSED GRAPHS
M. CALDAS(1), S. JAFARI(2), R. M. LATIF(3), T. NOIRI(4)
In this paper, we study some properties of functions with strongly α-closed graphs by utilizing α -open sets and the α -closure operator.
PRESQUE CONTRE-CONTINUITE DANS LES STRUCTURES FLOUES MINIMAUX
MIHAI BRESCAN, CONSTANTIN G. POPA
Le but du notre travail este de généraliser pour une structure floue minimale le concept de fonction presque contre-continue introduit dans la Topologie générale par Takashi Noiri et Valeriu Popa. Les plus importants résultats sont les théorèmes de caractérisations et les liaisons entre les différentes forme de presque contre-continuité et de faible continuité.
ON THE MARKOV-KAKUTANI'S FIXED POINT THEOREM
M. ALIMOHAMMADY(*), M. ROOHI(**), L. GHOLIZADEH(***)
This note deals with Markov-Kakutani's fixed point theorem in respect of compact p-star shaped subset of a topological vector space. In fact, it will be proved that every commutative family of continuous p-affine self mappings on a compact p-star shaped subset of a topological vector space has a common fixed point.
THE REMAINDER TERM OF SOME QUADRATURE FORMULAE
ANA MARIA ACU(1), ARIF RAFIQ(2), CARMEN VIOLETA MURARU(3)
In this paper we give some new quadrature formulae and we derive the estimates for the remainder term. The optimality in the sense of Nikolski of some quadrature formulae is studied. A property of the intermediate point for the optimal quadrature formula is established.
COMMON FIXED POINTS OF FUZZY MAPPINGS
AKBAR AZAM(1), MUHAMMAD ARSHAD(2), MUHAMMAD SHAKEEL(2*)
We obtain common fixed point theorem for a pair, respectively for a sequence of fuzzy contractive type mappings, by using sequence of iterates. Our theorems extend recent results of Bose and Sahani [5] and of Vijayaraju and Mohanraj [16].
ABOUT SOME BIVARIATE OPERATORS OF SCHURER TYPE
MIRCEA D. FARCAŞ
In this paper, we will obtain a form of Bernstein-Schurer bivariate operators and finally we will give an approximation theorem for them.
COMMON FIXED POINT THEOREMS FOR R-WEAKLY COMMUTING MAPPINGS OF TYPE (Ag) IN UNIFORM SPACES
J. K. KOHLI(1), JEETENDRA AGGARWAL(2)
The notion of R-weak commutativity of type (Ag) and that of compatibility of a pair of self mappings is extended to the framework of uniform spaces and fixed point theorems concerning them are proved. The results obtained in the process generalize several known results in the literature including the recent results of V. Pant, R.P. Pant and others and have a bearing on a problem of B.E. Rhoades.
COMMON FIXED POINTS IN CONVEX 2-METRIC SPACES
SANJAY KUMAR
In this paper, we introduce the concept of convex 2-metric spaces and present a generalization of Banach contraction principle in this newly defined space. Our result is a generalization of some well known results of 2-metric spaces. In 1970 Takahashi [4] introduced the notion of convex metric spaces and studied some fixed point theorems for non-expansive mappings in this space. Gahler [1] introduced the concept of 2-metric space alike to metric space. The purpose of this paper is to introduce the concept of convex 2-metric space analogue to convex metric space and obtain a generalization of Banach contraction principle in this space.
BOUNDEDNESS OF MULTILINEAR SINGULAR INTEGRAL OPERATOR WITH NON-SMOOTH KERNEL ON L<sup>p</sup> SPACES WITH VARIABLE EXPONENT
LANZHE LIU
In this paper, the boundedness for some multilinear operators related to some singular integral operator with non-smooth kernel on Lp spaces with variable exponent is obtained by using a sharp estimate of the multilinear operators.
ON THE MINIMAL WEAK UPPER GRADIENT OF A BANACH-SOBOLEV FUNCTION ON A METRIC SPACE
MARCELINA MOCANU
We prove that every function belonging to a Sobolev-type space N1,B(X) on a metric measure space X has a B-weak upper gradient in B that is pointwise minimal μ - almost everywhere, provided that the Banach function space B has a strictly convex and strictly monotone norm. This result generalizes corresponding known results involving Lebesgue spaces B = Lp(X), p > 1 [16] or, more general, Orlicz spaces B = LΨ (X) [17] with a strictly convex Young function Ψ satisfying a Δ2 - condition.
THE SPEED OF CONVERGENCE OF THE RIEMANN SUMS WITH APPLICATIONS TO GAMMA FUNCTION
CRISTINEL MORTICI
The purpose of this paper is to establish some results about the convergence speed of the Riemann sums and to use them to give some properties related with Gamma function. A new proof of the Stirling's formula is given, then we pass to the continuous case, using the Croft's lemma.
GEOMETRIC ASPECTS OF CLASSICAL NONHOLONOMIC, SCLERONOMIC MECHANICAL SYSTEMS
VALER NIMINEŢ, VICTOR BLĂNUŢĂ
A classical nonholonomic, scleronomic mechanical system Σ(1.1) is considered, whose the evolution equations are (2.6.). We associate to system Σ a canonical semispray S* on the phases space TM and we use the differential geometry of Lagrange spaces to study the systems Σ.
MINIMAL STRUCTURES, PUNCTUALLY <i>m</i> - OPEN FUNCTIONS AND BITOPOLOGICAL SPACES
TAKASHI NOIRI(1), VALERIU POPA(2)
By using m-open functions from a topological space into an m-space, we establish the unified theory for several weak forms of open functions between bitopological spaces.
SOME MINIMAL HELICOIDAL SURFACES IN MINKOWSKI SPACE R<sub>1</sub><sup>3</sup>
ALINA-MIHAELA PATRICIU
A helicoidal surface is a surface obtained by rotating a curve around an axis and simultaneously translating the curve along that axis. In this paper we identify some minimal surfaces inside of three classes of helicoidal surfaces in the Minkowski space R13
STATIONARY POINTS FOR MULTIFUNCTIONS ON THREE METRIC SPACES
VALERIU POPA
In this paper we prove a general unique fixed point theorem for multifunctions on three metric spaces which generalize the main results from [3] and [4].
FLOW OF AN UNSTEADY DUSTY FLUID BETWEEN TWO OSCILLATING PLATES UNDER VARYING PULSATILE PRESSURE GRADIENT
B. C. PRASANNAKUMARA(*), B. J. GIREESHA, C. S. BAGEWADI
An analytical study of unsteady dusty fluid flow between two oscillating plates has been considered. The flow is due to influence of nontorsional oscillations of plates and pulsatile pressure gradient. Flow analysis is carried out using differential geometry techniques and exact solutions of the problem are obtained using Laplace Transform technique. Further graphs drawn for different values of Reynolds number and on basis of these the conclusions are given. Finally, the expressions for skin-friction are obtained at the boundaries.
THE GENERALIZED CEBYSEV TYPE INEQUALITY
ARIF RAFIQ(1), QAISER SHAHBAZ(1), ANA MARIA ACU(2)
A generalization of Pecaric's extension to the Montgomery's identity has been derived. The generalization is applicable for any weight functions. The generalized Cebysev type inequality has also been obtained.
COMMON FIXED POINT THEOREMS FOR PROBABILISTIC Φ- CONTRACTION MAPPINGS
R. A. RASHWAN
In this paper, we establish some common fixed point theorems for probabilistic Φ- contraction mappings on Menger spaces. Our results improve some known results.
CHARACTERISTIC PROPERTIES OF THE INDICATRIX GIVEN BY A RANDERS CHANGE
RYOTA SHIMIZU(1), MASASHI KITAYAMA(2)
C. Shibata [6] investigated the theory of a change which was called a β-change of Finsler metric. We study the behavior of indicatrices given by special β-changes, in particular by a Randers change.
THETA FUNCTION IDENTITIES ASSOCIATED WITH MODULAR EQUATION
BHASKAR SRIVASTAVA
Ramanujan gave simple theta function identities for different bases. We have considered the continued fraction given in section 1, eq. (1.7) which equals quotient of theta functions on base four. This continued fraction is also of Ramanujan and is analogous to his famous continued fraction R(q). In this paper we have given simple theta function identities on base four. These identities will be helpful in deducing modular equations.
MORE ON SLIGHTLY-β-CONTINUOUS FUNCTIONS
SANJAY TAHILIANI
β-continuity was introduced by Monsef et al. [1] and then the weak and strong forms of β-continuity are studied. In this paper, we obtain several new properties of slightly β-continuous function which is defined by Noiri [8].