Volume 28, No. 1 (2018)
Articles
GENERALIZED VERSION OF FUZZY δ-SEMICLOSED SET
ANJANA BHATTACHARYYA
The notions of fuzzy δ-semiopen and fuzzy δ-semiclosed set have been introduced in [5]. Taking this idea as a basic tool, we introduce the notion of fuzzy generalized δ-semiclosed set (fgδ-semiclosed set, for short). Then the mutual relationships between this set with fg-closed set [2, 3], fgs-closed set [3], fsg-closed set [3], fgβ-closed set [3], fβg-closed set [3] are established. Afterwards, we introduce and characterize fgδ-semiclosed function. In Section 4, a new type of idempotent operator, viz., generalized δ-semiclosure operator is introduced and studied some of its properties. Next we introduce and characterize fuzzy generalized δ-semicontinuous function and show that the composition of two fuzzy generalized δ-semicontinuous functions may not be so. In Section 5, we introduce and characterize fuzzy generalized δ-semiregular and fuzzy generalized -δseminormal spaces and also we prove the invariance of the propery of a fuzzy topological space of being generalized δ-seminormal, under fuzzy generalized δ-semiirresolute function. In the last section, we first introduce fuzzy generalized δ-semi T2-space and then three different types of fuzzy continuous-like functions are introduced and establish that the inverse image of fuzzy generalized δ-semi T2-space under these functions are fuzzy T2-spaces [13].
ON SASAKIAN MANIFOLDS SATISFYING CURVATURE RESTRICTIONS WITH RESPECT TO A QUARTER SYMMETRIC METRIC CONNECTION
ASHIS BISWAS(1), SUSANTA DAS(2) and KANAK KANTI BAISHYA(3)
The object of the present paper is to study a quarter symmetric connection ∇ in a Sasakian manifold admitting some curvature restrictions as R^{∇}⋅ω^{∇}=0 and ω^{∇}⋅S^{∇}=0, where ω is a generalized quasi-conformal curvature tensor.
ON DUAL TOPOLOGIES FOR FUNCTION SPACES OVER C_{\mu, \nu}
ANKIT GUPTA(1), RATNA DEV SARMA(2)
Dual topologies for function space topologies between generalized topological spaces are defined. The point-open topology, compact-open topology and (μ,ν)-topology on C_{\mu, \nu} (Y,Z) are shown to be family-open. The notions of splittingness and admissibility for such spaces are introduced. It is proved that a topology on C_{\mu, \nu} (Y,Z) is splitting (resp. admissible) if and only if its dual topology is splitting (resp. admissible). Similarly, a topology on OZ (Y) is splitting (resp. admissible) if and only if its dual topology on C_{\mu, \nu} (Y,Z) is so.
COMPACTNESS AND REGULARITY VIA MAXIMAL OPEN AND MINIMAL CLOSED SETS IN TOPOLOGICAL SPACES
AJOY MUKHARJEE(1), SANTANU RAUT(2) and KALLOL BHANDHU BAGCHI(3)
In this paper, we introduce and study the notion of maximal open cover which in turn leads us to define and study m-compact spaces. We prove that there always exists a maximal open cover in an infinite T₁ topological space. We also obtain some results on minimal c-regular and minimal c-normal spaces. We prove that a Hausdorff m-compact topological space is minimal c-normal.
SOME FORMS OF (1, 2)-CONTINUITY IN BITOPOLOGICAL SPACES
TAKASHI NOIRI(1) and VALERIU POPA(2)
In this paper, by using mg-closed sets [35] and M-continuity [41] in m-spaces, we obtain the unified definitions and properties for τ₁τ₂-continuity, (1,2)-semi-continuity, (1,2)-precontinuity, (1,2)-α-continuity, and (1,2)-semi-precontinuity in bitopological spaces.
A GENERAL FIXED POINT THEOREM FOR A SEQUENCE OF MAPPINGS IN G_p - COMPLETE METRIC SPACES
VALERIU POPA(1) and ALINA-MIHAELA PATRICIU(2)
In this paper, a general fixed point theorem for a sequence of mappings in G_p - complete metric spaces is proved.
A GENERAL FIXED POINT THEOREM FOR TWO PAIRS OF MAPPINGS SATISFYING A ϕ-IMPLICIT RELATION IN 0 - COMPLETE PARTIAL METRIC SPACES
VALERIU POPA(1) and ALINA-MIHAELA PATRICIU(2)
In this paper a general fixed point theorem for two pairs of mappings satisfying a φ - implicit relation is proved. As application we obtain a fixed point theorem for a sequence of mappings in 0 - complete partial metric spaces, different by results from [24]
SPLINES FOR THE SET FUNCTIONS
VASILE POSTOLICĂ
Following the multiple possibilities to approximate any set function using proper sequenc-es of countable additive set - functions and our main conclusions given in some previous research works concerning the best approximation, we present the adequate splines for the countable additive set - functions. This work is a sequel by completion of the most im-portant results contained in the corresponding references.
FIXED POINT THEOREMS FOR GENERALIZED CONTRACTIVE AND EXPANSIVE TYPE MAPPINGS OVER A C* - ALGEBRA VALUED METRIC SPACE
KUSHAL ROY(1) and MANTU SAHA(2)
In this paper, fixed points of generalized contractive mappings and n-times reasonable expansive mappings over a C^{∗}-algebra valued metric space have been investigated. The results obtained so far are the existence of fixed points of generalized contractive mappings via the notion of d-point of a lower semi-continuous function on the underlying space. Also a result on coincidence point of two mappings has been established. Some examples are given in support of fixed points of expansive mappings.
ON THE GROWTH OF SOLUTIONS OF HOMOGENEOUS AND NON-HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS
MANSOURIA SAIDANI, BENHARRAT BELAȈDI
In this paper, we investigate the growth of solutions of higher order linear differential equations f^{(k)}+A_{k-1}(z)f^{(k-1)}+⋯+A₁(z)f′+A₀(z)f=0 and f^{(k)}+A_{k-1}(z)f^{(k-1)}+⋯+A₁(z)f′+A₀(z)f=F(z), where A₀(z)≡0, A₁(z),⋯,A_{k-1}(z) and F(z)≡0 are meromorphic functions of finite iterated p-order. We improve and extend some results of papers [1] and [5] by using the concept of the iterated order and considering the growth of some arbitrary dominant coefficient A_{s} (s=0,1,⋯,k-1) instead of A₀.
PSEUDO CL-SUPERCONTINUOUS FUNCTIONS AND CLOSEDNESS/COMPACTNESS OF THEIR FUNCTION SPACES
D. SINGH(1), JEETENDRA AGGARWAL(2) and J. K. KOHLI(3)
A new class of functions called `pseudo cl-supercontinuous' functions is introduced. Basic properties of pseudo cl-supercontinuous functions are studied and their place in the hierarchy of variants of continuity which already exist in the mathematical literature is discussed. The interplay between topological properties and pseudo cl-supercontinuity is investigated. Function spaces of pseudo cl-supercontinuous functions are considered and sufficient conditions for their closedness and compactness in the topology of pointwise convergence are formulated.
APPLICATIONS OF WEAK-BISPLIT GRAPHS
MIHAI TALMACIU
In this paper, using weak-decomposition, we give necessary and sufficient conditions for a graph to be weak-bisplit cograph. We also give we give some applications in optimization problems.
APPROXIMATE DIFFERENTIABILITY IN NEWTONIAN SPACES BASED ON BANACH FUNCTION SPACES
MARCELINA MOCANU
In this note we investigate the approximate differentiability of Newtonian functions on a doubling metric measure space. The Newtonian space under consideration consists of functions belonging to a rearrangement invariant Banach function space E and possesing an upper gradient which also belongs to E. Our main tools are a Poincaré inequality and a noncentered maximal operator, both defined via the Banach function space E. Under our assumptions, considering for a Newtonian function u an upper gradient g belonging to the given Banach function space E, it turns out that a Hajłasz gradient of u is a constant mul-tiple of the maximal function M_{E}g, which is Borel measurable and finite almost eve-rywhere.