Volume 33, No. 1 (2023)

SOME REMARKS ON BIHARMONIC QUADRATIC MAPS BETWEEN SPHERES

RAREȘ AMBROSIE

In this note, we prove a characterization formula for biharmonic maps in the Euclidean spheres of radius R, whose image lies in a small hypersphere. This formula represents a generalization of a result in E. Loubeau, C. Oniciuc, On the biharmonic and harmonic indices of the Hopf map, Trans. Amer. Math. Soc. 359 (2007). Then we apply it for quad-ratic maps between spheres.

ON p-OPEN SETS AND p*-URYSOHN SPACES

KALLOL BHANDHU BAGCHI

In this article we introduce the notions of p* - T1 space, p* - T2 , p*-regular space and p*-Urysohn space, an analogue of the classical notion of T1 space, T2 space, regular space and Urysohn space respectively, where the role of open sets (resp., of the corresponding closure operator Cl) is played by p-open sets (resp., by the corresponding p-closure operator Cl p ). It is seen that the notion of p*-Urysohn space is stronger than each of the notion Urysohn space, pre-Urysohn space, p-Urysohn space and weakly Hausdorff space. The notion of ordered pair of pre-open sets in a topological space is introduced along with and some important and interesting results have been obtained. Using p-open sets, one can introduce and study various notions in topological spaces.

COMPLEX DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS OF FINITE (α,β)- ORDER

BENHARRAT BELAÏDI(1), TANMAY BISWAS(2)

In this paper, we wish to investigate the complex higher order linear differential equations in which the coefficients are entire functions of (α,β)- order and obtain some results which improve and generalize some previous results of Tu et al. [33] as well as Belaïdi [2, 3, 4].

FUZZY p*-PRECOMPACT TOPOLOGICAL SPACES

ANJANA BHATTACHARYYA

In this paper a new type of compactness in fuzzy topological spaces is introduced and studied by using p*-preopen sets [1] as a basic tool. We characterize this newly defined compactness by fuzzy net and prefilterbase. It is shown that this compactness implies fuzzy almost compactness [3] and the converse is true only on fuzzy p*-preregular spaces [1]. Afterwards, it is shown that this compactness remains invariant under fuzzy p*-preirresolute functions [1].

A MEAN ERGODIC THEOREM IN A SUBALGEBRA OF GENERALIZED WEIGHTED GRAND LEBESGUE SPACES

ILKER ERYILMAZ

The paper introduces a new type of grand Lebesgue space, for which special cases are weighted grand Lebesgue spaces introduced by Fiorenza, Gupta and Jain (2008) and a generalization of grand Lebesgue spaces introduced by Greco, Iwaniec and Sbordone (1997). The main result is a mean ergodic theorem, in the Von Neumann sense, for some operator acting on the closure of the set of compactly supported in the newly introduced grand Lebesgue space.

SIR DYNAMICAL MODEL WITH DEMOGRAPHY AND LAGRANGE-HAMILTON GEOMETRIES

MIRCEA NEAGU(1), ADRIANA VERONICA LITRĂ(2)

The aim of this paper is to develop, via the least squares variational method, the La-grange-Hamilton geometries (in the sense of nonlinear connections, d-torsions and La-grangian Yang-Mills electromagnetic-like energy) produced by the SIR dynamical system with demography in epidemiology. From a geometrical point of view, the Jacobi instabil-ity of this SIR dynamical system with demography is established. At the same time, some possible epidemiological and demographic interpretations are also derived.

UPPER AND LOWER LPT mI-CONTINUOUS MULTIFUNCTIONS

TAKASHI NOIRI(1), VALERIU POPA(2)

We introduce the notions of upper/lower (τ, m)-J-continuous multifunctions and obtain many characterizations of such multifunctions. The notion is obtained from a multifunc-tion F :(X, τ ) → (Y, σ, J) and several generalizations of J-open sets on the ideal topological space (Y, σ, J). If F is single valued, m = σ and J = {∅}, then the above multifunction is a (τ, m)-continuous function.

A GENERAL FIXED POINT THEOREM FOR MAPPINGS IN ORBITALLY COM-PLETE S – METRIC SPACES

VALERIU POPA(1), ALINA-MIHAELA PATRICIU(2)

The purpose of this paper is to extend Theorem 5 [18] to a S - metric space, without orbit-ally continuity, generalizing Theorem 4 [2], Theorems 1-4, 6-8 [11], Corollary 2.19 and 2.21 [23], Theorems 23, 24 [20], Theorems 3.2-3.4 [21] and to obtaining a Ćirić-Jotić-type result in S - metric spaces.