Volume 26, No. 2 (2016)
Articles
SOME GENERALIZATIONS OF ULTRA CONTINUOUS MULTIFUNCTIONS
TAKASHI NOIRI(1) and VALERIU POPA(2)
We introduce the notion of upper/lower (τ,m)-continuous multifunctions and obtain many characterizations of such multifunctions. The notion of upper/lower (τ,m)-continuous mul-tifunctions is a generalization of (τ,m)-continuous functions (V. Popa and T. Noiri, Rend Circ. Mat. Palermo (2) 51 (2002), 295-316) and upper/lower ultra continuous multifunc-tions due to Navalagi et al (G. B. Navalagi, M. Lellis Thivagar and R. Raja Rajeswari, Indian J. Math. Comput. Sci. Inform. Techn. 1(1) (2008), 69-74).
A STRICT FIXED POINTS FOR MULTIFUNCTIONS SATISFYING A GENERAL-IZED IMPLICIT GREGUŠ TYPE CONDITION IN SYMMETRIC SPACES AND APPLICATIONS
VALERIU POPA(1) and ALINA-MIHAELA PATRICIU(2)
In this paper a general fixed point theorem of generalized Greguš type in symmetric spac-es for hybrid pair satisfying a new type of implicit relation using generalized altering dis-tance and we obtain simultaneous results for contractive and extensive mappings. As ap-plication, new results for hybrid pairs satisfying contractive and expansive conditions of integral type are obtained.
ON BICLIQUES, BICLIQUE PARTITIONS AND RELATED CLASSES OF COGRAPHS
MIHAI TALMACIU
In this article we will highlight the relation between attack graphs, cross associations and biclique partitions. The attack graphs are used to evaluate network security risk. Also, we will give an efficient recognition algorithm for a maximal subclass of cographs (P4-free graphs), we will give the necessary and sufficient conditions for the existence of a bicli-que partition and we will determine some combinatorial optimzation numbers for some classes of graphs (maximum subclasses for P4-free) in efficient time. Also, we will deter-mine maximum bicliques for a maximal subclass of cographs and we give some applicati-ons of minimal unbreakable graphs in optimization problems and in chemistry. Bicliques (complete bipartite graphs) of graphs have been studied extensively, partially motivated by the large number of applications.
RECOGNITION ALGORITM FOR P₄-TIDY GRAPHS
MIHAI TALMACIU
In this article we give a characterization of P₄-tidy graphs. We also give recognition algorithm for P₄-tidy graphs, comparable to existent ones as execution time. Finally, we determine the combinatorial optimization number in efficient time for P₄-tidy graphs. We show that for P4-tidy graphs clique problem is polynomial time.
A CHARACTERIZATION OF ORLICZ-POINCARÉ INEQUALITY ON METRIC MEASURE SPACES
MARCELINA MOCANU
In this note we characterize a weak Orlicz-Poincaré inequality through the Hölder conti-nuity of locally integrable functions possessing upper gradients in the corresponding Or-licz space, under some growth assumptions on the Young function. Our results are proved in the setting of doubling metric measure spaces.
NOTE ON THE ITERATES OF q- AND (p,q)-BERNSTEIN OPERATORS
VOICHIŢA ADRIANA RADU
In this note we are concerned with the limit behavior of the iterates of q and (p,q)-Bernstein operators. The convergence of the iterates of q-Bernstein operators was proved by H. Oruç and N. Tuncer in 2002 and by X. Xiang, Q. He and W. Yang in 2007, using the q-differences, Stirling polynomials and matrix techniques and by S. Ostrovska in 2003, with the aids of eigenvalues. We try to prove the convergence from some different points of view: using contraction principle (Weakly Picard Operators Theory). The theory of (weakly) Picard operator is very useful to study some properties of the solutions of those equations for which the method of successive approximations works.
fgs* - CLOSED SETS AND fgs*-CONTINUOUS FUNCTIONS IN FUZZY TOPO-LOGICAL SPACES
ANJANA BHATTACHARYYA
In this paper, we introduce and study a new type of fuzzy generalized closed set and fuzzy generalized continuity in a fuzzy topological space. Also it is shown that fuzzy compactness and fuzzy normality remain invariant under this newly defined continuous function. Afterwards, a new type of fuzzy closure operator is introduced which is an idempotent operator which is distributive over union but not over intersection. Lastly, we introduce and characterize fgs*-closed (resp., fgs*-open) function which is weaker that of fgs-closed (resp. fgs-open) function.
GROWTH AND OSCILLATION OF SOLUTIONS TO HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS WITH COEFFICIENTS OF FINITE LOGARITH-MIC ORDER
AMINA FERRAOUN(1) and BENHARRAT BELAÏDI(2)
In this paper, we study the growth of solutions of complex higher order linear differential equations with entire or meromorphic coefficients of finite logarithmic order. We extend some precedent results due to L. Kinnunen; B. Belaïdi; J. Liu, J. Tu and L. Z. Shi; H. Hu, X. M. Zheng; T. B. Cao, K. Liu and J. Wang and others. We also consider the fixed points of solutions in this paper.
UPPER AND LOWER COMPLETELY CONTINUOUS MULTIFUNCTIONS
J. K. KOHLI(1) and C. P. ARYA(2)
The notion of complete continuity of functions (Kyungpook Math. J. 14(1974), 131-143) is extended to the realm of multifunctions. Basic properties of upper (lower) completely continuous multifunctions are studied and their place in the hierarchy of variants of con-tinuity of multifunctions is elaborated. Examples are included to reflect upon the distinc-tiveness of upper (lower) complete continuity of multifunctions from that of other vari-ants of continuity of multifunctions which already exist in the literature. Interplay be-tween topological properties and completely continuous multifunctions is considered.
GROWTH RATES OF COMPOSITE ENTIRE AND MEROMORPHIC FUNCTIONS IN THE DIRECTION OF THEIR RELATIVE L*-ORDERS
SANJIB KUMAR DATTA(1) and TANMAY BISWAS(2)
In this paper we establish some newly developed results regarding the growth rates of composite entire and meromorphic functions on the basis of their relative L*-order and relative L*-lower order..
ON PAIRWISE s-COMPACT SPACES
AJOY MUKHARJEE(1), ARUP ROY CHOUDHURY(2) AND M. K. BOSE(3)
We introduce and study the notion of pairwise s-compact spaces in bitopological spaces. The notion of pairwise s-compactness is stronger than the notion of pairwise compactness.