Volume 20, No. 1 (2010)

Articles

STRONGLY AND PERFECTLY CONTINUOUS MULTIFUNCTIONS
J.K. KOHLI(1), C.P. ARYA(2)

The notions of strong continuity of Levine (Amer. Math. Monthly 67(1960), 269) and perfect continuity due to Noiri (Indian J. Pure Appl. Math. 15(3) (1984), 241-250) are extended to the framework of multifunctions. Basic properties of strongly continuous and upper (lower) perfectly continuous multifunctions are studied and their place in the hierarchy of variants of continuity of multifunctions is discussed. The class of upper (lower) perfectly continuous multifunctions properly contains the class of strongly continuous multifunctions and is strictly contained in the class of upper (lower) cl-supercontinuous multifunctions (Applied Gen. Topol.)[5]. Examples are included to reflect upon the distinctiveness of the notions so introduced from the ones that already exist in the mathematical literature. In the process we extend several known results in the literature including those of Ekici, Singh and others to the realm of multifunctions.

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ON ALMOST λ-CONTINUOUS FUNCTIONS
S. JAFARI(1), S. P. MOSHOKOA(2), K. R. NAILANA(3), T. NOIRI(4)

In the paper we introduce a new class of functions between topological spaces, namely almost λ-continuous functions and present some properties for these functions.

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AN APPLICATION OF COMPLEX LEGENDRE TRANSFORMATION TO V-COHOMOLOGY GROUPS
CRISTIAN IDA

In this paper, using the Lagrangian-Hamiltonian formalism (L-dual proces) on the holomorphic tangent bundle of a complex Lagrange space (M, L), we obtain similar results as in [10] concerning to v-cohomology groups of a complex Hamilton space (M,H). Finally we study a relative vertical cohomology associated to complex Legendre transformation.

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EMBRYONIC GENETIC ALGORITHM WITH RANDOM GENERATIONAL GROWING STRATEGY FOR OPTIMIZING VARIABLE ORDERING OF BDDS
OCTAV BRUDARU(1), IULIAN FURDU(2), RÜDIGER EBENDT(3)

This paper addresses the problem of optimizing the variable ordering in Binary Decision Diagrams (BDDs). A new hybrid embryonic genetic algorithm is proposed for optimizing the variable ordering that combines a branch & bound technique with the basic genetic algorithm. It uses fitness based on a lower bound and embryos instead of full chromosomes. A novel growing technique introduces two new growing operators. The results of an experimental evaluation demonstrate the efficiency of the approach.

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WELL-POSEDNESS OF A FIXED POINT PROBLEM USING G-FUNCTIONS
MOHAMED AKKOUCHI(1), VALERIU POPA(2)

We study the well-posedness of the fixed point problem for asymptotically regular self-mappings of a metric space (X, d) which satisfy a contractive condition (see inequality (2.1)) defined by a G-type function (see [5]). So, in particular, our result provides some improvements to a result of [5].

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FIXED POINTS OF EXPANSION MAPS IN INTUITIONISTIC FUZZY METRIC SPACES
SUNEEL KUMAR(1), SERVET KUTUKCU(2)

The purpose of this paper is to prove some fixed point and common fixed point theorems for expansion maps in intuitionistic fuzzy metric spaces. The main result has been proved for two pairs of non-surjective expansion maps on noncomplete intuitionistic fuzzy metric space through weak compatibility. Our results extend, generalize and intuitionistic fuzzify several fixed point theorems on metric spaces, Menger PM-spaces and fuzzy metric spaces.

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SOME PROPERTIES OF A R-RANDERS QUARTIC SPACE
OTILIA LUNGU, VALER NIMINEŢ

It is well known that a Randers metric is a deformation of a Riemannian metric using a 1-form. In this paper we consider a deformation of a 4-th root metric (or a quartic metric) using the Riemannian metric. We call it a R-Randers quartic metric and we are going to study some of its properties.

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ORLICZ-POINCARE INEQUALITIES AND EMBEDDINGS OF ORLICZ-SOBOLEV SPACES ON METRIC SPACES
MARCELINA MOCANU

The main result of this paper shows that an Orlicz-Sobolev space with zero boundary values on a doubling metric measure space with homogeneous dimension s, corresponding to an Orlicz function generalizing tq with q < s, is continuously embedded in an Orlicz space generalizing Lq*, where q* = sq/(s-q). In order to prove this embedding result, we use an optimal result of Heikkinen [18] describing sharp self-improving properties of Orlicz-Poincare inequalities in connected metric spaces. We also prove an Orlicz-Poincare inequality for functions vanishing on large subsets of balls and some counterparts of the results mentioned above for Orlicz-Sobolev spaces of Hajlasz type.

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IMPROVED ESTIMATORS FOR BIG FACTORIALS
CRISTINEL MORTICI

The aim of this paper is to introduce some new estimators for big factorials connected to Stirling and Burnside formula. Some results stated by Mortici in [A method which generates sharp estimations for big factorials J. Adv. Math. Studies 1(2008) 71-74] are extended.

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THE GEOMETRIZATION OF LAGRANGE DYNAMICAL SYSTEMS
VALER NIMINEŢ, OTILIA LUNGU

A mechanical system Q generated by a Lagrangian L(t, x, x' ) is considered, whose the evolution equations is described by the Euler-Lagrange equations (2.1.). The geometry of the dynamical system determined by Q is the geometry of a semispray whose integral curves are the evolution equations of Q. The theory is extended to Lagrangians of higher order.

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A UNIFIED THEORY OF ALMOST CONTINUITY FOR MULTIFUNCTIONS
TAKASHI NOIRI(1), VALERIU POPA(2)

We introduce the notions of upper/lower almost m-continuity for multifunctions from a set satisfying certain minimal condition into a topological space. We obtain their characterizations and properties which unify those of almost continuity, almost quasi-continuity, almost precontinuity, almost &alpha;-continuity, almost &beta;-continuity and almost &gamma;-continuity for multifunctions.

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COMMON FIXED POINT FOR COMPATIBLE PAIRS OF MAPPINGS IN NON-COMPLETE METRIC SPACES
NEERAJ ANANT PANDE(1), J.ACHARI(2), PRACHI R. AGRAWAL(3)

We prove the existence and uniqueness of a common fixed point for two compatible pairs of self-maps of a metric space. Instead of the completeness of the metric space, we use a weaker assumption, namely, the convergence of alternate images of an associated sequence. Our main result generalizes several known results from [1], [3], [4] and [5].

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A NOTE ON ALMOST s - CONTINUITY
UĞUR ŞENGŰL

T. Noiri, M. B. Ahmad and M. Khan introduced the notion of almost s-continuous functions [20] since then the function studied by various authors [1,4,11] Continuing in the spirit of this papers we obtain several properties and new characterizations of almost s-continuous functions. We improve and strengthen some of the known results. The concept of co-SR-closed graph is introduced.

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