Volume 29, No. 1 (2019)
Articles
<em>f</em>ğ-CLOSED SETS IN A FUZZY SET TOPOLOGY
ANJANA BHATTACHARYYA
This paper deals with a new type of fuzzy generalized version of closed sets, called fğ-closed sets, which is already defined in [16]. Again the mutual relationships of this class of sets with other classes defined in [3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16] are established. Then a new type of closure operator, called fğ-closure operator, is introduced and it is proved that this is an idempotent operator. With the help of this operator, fğ-open, fğ-closed, fğ-continuous and fğ-irresolute functions are introduced and characterized. Afterwards, fğ-regular, fğ-normal, fğ-compact, fğ-T2-spaces are introduced and characterized. Lastly, applications of the above mentioned functions on these spaces are given.
GENERALIZED CLOSED SET AND GENERALIZED CONTINUITY IN FUZZY M-SPACE
ANJANA BHATTACHARYYA
This paper deals with a generalized version of fuzzy closed sets in fuzzy m-spaces [2]. Using this concept as a basic tool, we introduce a generalized version of closed and open functions in fuzzy m-spaces. Several characterizations of these functions are proved. Moreover, a generalized version of continuity in fuzzy m-space is introduced and studied. Afterwards, several applications of this type of function are given in the study of general-ized versions of fuzzy regular, fuzzy normal and fuzzy compact spaces, in the setting of fuzzy m-spaces.
A GENERAL CONNECTION ON SASAKIAN MANIFOLDS AND THE CASE OF ALMOST PSEUDOSYMMETRIC SASAKIAN MANIFOLDS
ASHIS BISWAS(1), KANAK KANTI BAISHYA(2)
The object of the present paper is to study necessary conditions for the existence of al-most pseudo symmetric and almost pseudo Ricci symmetric Sasakian manifolds admitting a new connection, named general connection. It is worthy to mention that such connec-tion reduces to quarter-symmetric connection, generalized Tanaka-Webster connection, Zamkovoy connection and Schouten-van Kampen connection as particular cases.
A NOTE ABOUT TRUNCATED RHOMBICUBOCTAHEDRON AND TRUNCATED RHOMBICICOSIDODECAHEDRON SPACE
TEMEL ERMIŞ(1), ÜMIT ZIYA SAVCI(2), OZCAN GELIŞGEN(3)
The theory of convex sets is a vibrant and classical field of modern mathematics with rich applications. If every point of a line segment that connects any two points of the set are in the same set, then it is convex. The more geometric aspects of convex sets are developed introducing some notions, but primarily polyhedra. A polyhedra, when it is convex, is an extremely important special solid in R^n. Some examples of convex subsets of Euclidean 3-dimensional space are Platonic Solids, Archimedean Solids and Archimedean Duals or Catalan Solids. In this study, we give two new metrics, their spheres being a truncated rhombicuboctahedron and a truncated rhombicicosidodecahedron.
A NEW CONTRACTION-LIKE MULTIVALUED MAPPING ON GEODESIC SPACES
EMIRHAN HACIOĞLU(1), VATAN KARAKAYA(2)
Abstract.We define a new class of multivalued mappings and prove existence, stability of fixed point sets and convergence results for this class of multivalued hybrid mappings in CAT(k) spaces which are more general than Hilbert spaces and CAT(0) spaces. We also show with an example that this class is not included in the class of multivalued nonexpan-sive mappings, however, interestingly, we see that multivalued version of Thianwan itera-tion is built with this mapping and is strong convergent to its fixed point.
ON SOME FORMS OF OPEN FUNCTIONS IN IDEAL TOPOLOGICAL SPACES
TAKASHI NOIRI(1), VALERIU POPA(2)
We introduce the notion of mIO(X)-structures determined by operators Int, Cl and Cl * on an ideal topological space (X; τ , I). By using mIO(X)-structures, we introduce and investigate a function f : (X; τ) → (Y; σ; I) called mI-open. As special cases of mI-open functions, we obtain properties of semi-I-open [8], pre-I-open [1], α-I-open [1], b-I-open [2], β-I-open [1], weakly semi-I-open [5], and weakly-b-I-open [13] functions.
A FIXED POINT THEOREM FOR HYBRID PAIRS SATISFYING A NEW TYPE OF LIMIT RANGE PROPERTY IN SYMMETRIC SPACES AND APPLICATIONS
VALERIU POPA
A general fixed point theorem for two pairs of hybrid mappings satisfying a new type of limit range property in symmetric spaces is proved, generalizing Theorem 2 and Theorem 3 [7]. As application, we obtain new results for hybrid mappings satisfying contractive conditions of integral type and for mappings satisfying φ- contractive condi-tions.
GENERAL RELATED FIXED POINT THEOREM FOR TWO PAIRS OF MAP-PINGS IN TWO METRIC SPACES
VALERIU POPA(1), ALINA-MIHAELA PATRICIU
In this paper a general fixed point theorem for two pairs of mappings in two metric spaces, which generalizes the results from [2] and [7], is proved.
ISAC’S CONES FOR THE SET FUNCTIONS WITH BOUNDED p-VARIATION
VASILE POSTOLICĂ
This research work is devoted to present original Isac’s Cones for the set functions with bounded p-variation, having main applications in the General Efficiency and also in the Best Approximation.
ON THE COINCIDENCE AMONG ORLICZ-SOBOLEV SPACES ON METRIC SPACES
MARCELINA MOCANU
We generalize a coincidence result from the case of Sobolev-type spaces to the case of Orlicz-Sobolev spaces corresponding to a doubling Young function, in the setting of doubling metric measure spaces. We consider three types of Orlicz-Sobolev spaces: (i) a space of Newtonian type; (ii) a space associated to a generalized Poincaré inequality; (iii) a space defined as the closure of the class of Orlicz functions that are locally Lipschitz, under some norm involving an abstract differential operator.