Volume 29, No. 2 (2019)
Articles
ON A WEAKER FORM OF MINIMAL OPEN SETS AND A STRONGER FORM OF MEAN OPEN SETS
KALLOL BHANDHU BAGCHI
In this paper, we introduce the notions of locally minimal open (resp. locally minimal closed) and s-mean open (resp. s-mean closed) sets at a certain point in a topological space and investigate some properties of such sets. We see that a minimal open (resp. minimal closed) set is locally minimal open (resp. locally minimal closed) at each of its points and the notion of s-mean open (respectively, s-mean closed) sets is stronger than the notion of mean open (respectively, mean closed) sets.
FUZZY PRE - γ -CONTINUOUS AND ALMOST PRE- γ-CONTINUOUS FUNCTIONS
ANJANA BHATTACHARYYA
In this paper we first introduce a new type of fuzzy open-like set, viz., fuzzy pre-γ-open set, the collection of which is strictly larger than that of fuzzy open set. Afterwards, two new types of fuzzy continuous-like functions, viz., fuzzy pre- γ -continuous and fuzzy almost pre- γ -continuous functions are introduced and studied. It is shown that fuzzy almost pre- γ -continuous function is fuzzy pre- γ -continuous and the converse is true on-ly in fuzzy pre- γ -regular space.
SOME TOPOLOGICAL ASPECTS IN m-METRIC SPACES
SUSHANTA KUMAR MOHANTA(1), DEEP BISWAS(2)
In this paper, we introduce a new class of open balls in an m-metric space (X; μ) which will form a base for a Hausdorff topology on X. This will facilitate the initiation of open and closed sets, neighbourhoods and other allied notions in m-metric spaces. Moreover, we discuss the regularity and first countability properties of m-metric spaces and prove Cantor's intersection theorem, Baire's category theorem, Urysohn's lemma in the setting of m-metric spaces.
UPPER AND LOWER m-I-CONTINUOUS MULTIFUNCTIONS
VALERIU POPA(1), TAKASHI NOIRI(2)
In this paper we introduce upper/lower m-I-continuous multifunctions as multifunctions defined on an ideal minimal space (X; m; I). We obtain some characteriza-tions and several properties of such multifunctions. As special cases of these properties, we obtain the properties of upper/lower α-I-continuous [4], upper/lower semi-I-continuous [3] and upper/lower pre-I-continuous [3] multifunctions.
A STRONG CONVERGENCE OF A MODIFIED KRASNOSELSKII-MANN AL-GORITHM FOR A FINITE FAMILY OF DEMICONTRACTIVE MAPPINGS IN BANACH SPACES
T.M.M. SOW
In this paper we propose an iterative algorithm, which is based on the Krasnoselskii-Mann iterative algorithm for fixed point problems of a finite family of demicontractive map-pings in the setting of real Banach spaces. We prove that the sequence generated by the proposed method converges strongly to a common fixed point of a finite family of demicontractive mappings which is also the solution of a variational inequality. The iterative algorithm and results presented in this paper generalize, unify and improve some previously known results of this area.
λ-EDGE SPAN OF SOME ALMOST REGULAR GRAPHS
M. MURUGAN(1), P. SRIRAMAN(2), M. SURIYA(3)
In this paper we introduce the notion of λ- edge span of a graph, where λ is the λ -number or L(2; 1) labeling number of a graph. Also, we introduce the concept of almost regularness for infinite graphs. An infinite graph is almost regular if it is regular except for a finite number of points. Here, we consider some important infinite graphs which are al-most regular and find the λ -number and λ -edge span of them.
SELECTION PROPERTIES OF QUASI-UNIFORM SPACES USING IDEALS
RITU SEN
In this paper we study the properties of Pre Hurewicz spaces modulo I, I-Hurewicz bounded spaces, Pre Menger spaces modulo I and I-Menger bounded spaces. Relation-ships among such spaces are also being investigated thereafter.
Ḡα-CLOSED SETS IN TERMS OF GRILLS
A. SELVAKUMAR(1), S. JAFARI(2)
In this paper we introduce the new notions of ḡα (θ)-convergence and ḡα (θ)-adherence of a grill in a topological space. We prove necessary and sufficient conditions for a grill to be ḡα (θ)-adherent to a point, respectively ḡα (θ)-convergent to a point, then we provide a characterization of relative ḡα (θ)-closedness of a set in terms of grills.
A CONTRIBUTION ON CONVEX AND STRICTLY PLURISUBHARMONIC FUNCTIONS DEFINED BY HOLOMORPHIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES AND APPLICATIONS
ABIDI JAMEL
Let $A_1, A_2\in\mathbb{C}\backslash\{0\}$ and $n, m\in\mathbb{N}\backslash\{0\}.$ Using algebraic methods, we prove that there exist three analytic functions $\varphi:\mathbb{C}^m\rightarrow\mathbb{C}$ and $g_1, g_2:\mathbb{C}^n\rightarrow\mathbb{C}$ such that $v$ is convex and strictly plurisubharmonic on $\mathbb{C}^n\times\mathbb{C}^m$ if and only if $m=1,$ $n\in\{1, 2\},$ there exists $c\in\mathbb{C}$ such that $\mid\varphi+c\mid^2$ is convex and strictly subharmonic on $\mathbb{C}$ and the functions $g_1$ and $g_2$ have fundamental representations over $\mathbb{C}^n.$ $v(z,w)=\mid A_1\varphi(w)-overline{g_1}(z)\mid^2+\mid A_2\varphi(w)-\overline{g_2}(z)\mid^2,$ for $(z,w)\in\mathbb{C}^n\times\mathbb{C}^m.$ At the end, we prove an additional theorem by analytic and algebraic methods.
CONSTRUCTIVE ORDERED ALGEBRAIC STRUCTURES
MARIAN ALEXANDRU BARONI
Ordered algebraic structures are examined within the framework of Bishop-style con-structive mathematics. In the constructive approach, the partial order is replaced by the classically equivalent, but constructively stronger, notion of co-order. While one could define an ordered algebraic structure by requiring certain properties of monotonicity of the algebraic operations, the constructive counterpart of strong mono-tonicity could be more appropriate for a constructive examination.