Volume 31, No. 2 (2021)
Articles
COMMON COUPLED FIXED POINT THEOREM FOR HYBRID PAIR OF MAP-PINGS SATISFYING φ − ψ CONTRACTION ON NONCOMPLETE METRIC SPACE
BHAVANA DESHPANDE(1) and AMRISH HANDA(2)
We establish a coupled coincidence and common coupled fixed point theorem for hybrid pair of mappings under φ – ψ contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. We also give an example to validate our result. We improve and generalize several known results.
SOME GEOMETRICAL ASPECTS OF DYNAMICAL SYSTEMS WITH CONTROL
VALER NIMINEȚ
In this article, we discuss geometric controllability conditions for dynamical systems and study some particular cases of dynamical systems with control.
A NEW VIEWPOINT IN THE STUDY OF ⋆-CONTINUITY FOR MULTIFUNC-TIONS
TAKASHI NOIRI(1) and VALERIU POPA(2)
We introduce and study a unified form (called m⋆-Icontinuity) of ⋆-continuity [9], α(⋆)-continuity [10], β(⋆)-continuity [11] and other continuity properties for multifunctions in ideal topological spaces.
SOME RESULTS ON THE HYPER-ORDER OF SOLUTIONS OF HOMOGENE-OUS LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS
MANSOURIA SAIDANI(1) and BENHARRAT BELA¨IDI(2)
The purpose of this paper is the study of the growth of solutions of higher order linear differential equations f(k) + (Dk−1 + Bk−1eQk−1(z))f(k−1) + · · · + (D1 + B1eQ1(z)) f′ + (D0 + A1eP1(z) + A2eP2(z)) f = 0, where Ai(z) (̸≡ 0) (i = 1, 2), Bj(z) (̸≡ 0) (j = 1, ..., k − 1), Dm (z) (m = 0, ..., k−1) are meromorphic functions of finite order less than n, Pi (z) = ai,nzn+· · ·+ai,0 and Qj (z) = bj,nzn+· · ·+bj,0 are polynomials with degree n ≥ 1 such that ai,q, bj,q (i = 1, 2; j = 1, ..., k −1; q = 0, 1, ..., n) are complex numbers. Our results extend the previous results due to Habib and Bela¨ıdi [3], [11], [12] and Beddani and Hamani [4].
A NEW MENON-TYPE IDENTITY DERIVED FROM GROUP ACTIONS
MARIUS TĂRNĂUCEANU
In this short note, we give a new Menon-type identity involving the sum of element or-ders and the sum of cyclic subgroup orders of a finite group. It is based on applying the weighted form of Burnside’s lemma to a natural group action.
NEW TYPES OF FUZZY CONTINUITY VIA β-SEMIOPEN SETS
ANJANA BHATTACHARYYA
This paper deals with a new type of fuzzy open-like sets, viz., fuzzy β-semiopen sets, the class of which is strictly larger than that of fuzzy semiopen sets [1], but strictly smaller than the classes of fuzzy β-open sets [8], respectively of fuzzy e∗-open sets [4]. It is shown that the collection fuzzy β-semiopen sets does not form a fuzzy topology. In Sec-tion 4, a new type of continuous-like function, viz., fuzzy (β-semi, r)-continuous function is introduced and studied. In Section 5, some applications of this new type of function are established.
A NEW TYPE OF REGULAR SPACE VIA FUZZY PREOPEN SETS
ANJANA BHATTACHARYYA
In this paper we introduce a new closure-like operator in fuzzy topological spaces, via fuzzy preopen sets. Then mutual relationships of this operator with several closure opera-tors in fuzzy topological spaces, studied in [2, 3, 4, 6, 7, 8, 11, 12] are established. The newly introduced operator is idempotent in fuzzy spaces satisfying some regularity prop-erty with respect to this operator, but it is not idempotent in general. Some characteriza-tions of the new operator via nets are given in the last section.
INVARIANT POINTS AND ε-APPROXIMATIONS FOR MAPPINGS SATISFY-ING RATIONAL-TYPE CONTRACTIVE CONDITIONS IN TAKAHASHI SPACES
SUMIT CHANDOK(1) and T.D. NARANG(2)
In this paper, we prove some Brosowski-Meinardus type invariant point results for the set of ε-simultaneous approximation and ε-simultaneous coapproximation for rational type contraction mappings defined on Takahashi spaces. Subsequently, we deduce some re-sults on ε-approximation, ε-coapproximation, best approximation and best co-approximation for such class of mappings.
ON ω^c-SETS AND ω-SETS IN TOPOLOGICAL SPACES
AJOY MUKHARJEE
In this paper we introduce and study the notion of ω^c-set. We also study ω-sets, as complements of ω^c-sets. Finally, using the ω^c-sets and ω-sets of a topological space, we introduce and study the notion of ω-extremally disconnected topological spaces. We obtain a result akin to Urysohn’s Lemma in the setting of ω-extremally disconnected top-ological spaces.
ISOMETRY GROUPS OF TRUNCATED TETRAKIS HEXAHEDRON AND TRUNCATED TRIAKIS OCTAHEDRON SPACES
ZEYNEP CAN(1) and OZCAN GELIȘGEN(2)
The truncated tetrakis hexahedron and the truncated triakis octahedron are convex solids in the class Truncated Catalan solids. The aim of this work is to develop two new Min-kowski geometries by dTTH−metric and dTTO−metric which unit spheres are truncated tetrakis hexahedron and truncated triakis octahedron, respectively and to find their isometry groups. After we derive these metrics we also give some properties of them. Furthermore, we give that the group of isometries of the 3−dimensional analytical space furnished by dTTH−metric or dTTO−metric is the semi-direct product of octahe-dral group Oh and translation group T(3).