Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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From deterministic to stochastic equilibrium problems
Full text linkIn this paper, by means of Castaing representation Theorem, we extendthe results by M. Ait Mansour, R-.A. Elakri and M. Laghdir [Equilibriumand quasi-equilibrium problems under j-quasimonotonicity andj-quasiconvexity, Existence, stability and applications, Minimax Theoryand its Applications, 2 (2) (2017), 175–229] to random equilibrium problemswherein the objective data are subject to a random perturbation. Weobtain deterministic as well as random (or measurable) and integral solutionsto random equilibrium problems. The case when the random parameterhas a probability of realization suggests us to introduce stochasticformulations of equilibria covering the expected value approach and thealmost sure method. Thus, we prove the existence of two further kinds ofequilibria under uncertainty: almost sure solutions and expected stochasticequilibrium points. Finally, we present an application to stochasticquasiconvex programming for which we establish the existence of almostsure minimizers.Entrat
Zero divisor graphs of skew Hurwitz series rings
Full text linkFor a ring endomorphism , we investigate theinterplay between the ring-theoretical properties of the skewHurwitz series ring and the graph-theoreticalproperties of its zero-divisor graph . Furthermore, we examine the preservation of diameter and girthof the zero-divisor graph under extension to skew Hurwitz seriesrings
On complex H-type Lie algebras
Full text linkLet be a complex nilpotent Lie algebra equipped with aHermitian inner product . We show thatif is an H-type Liealgebra in the sense of Kaplan, then must be isomorphicto a complex Heisenberg Lie algebra. This shows that the class ofcomplex H-type Lie algebras is very small
Int-soft structures applied to ordered semihypergroups: Int-soft structures applied to ordered semihypergroups
Full text linkMolodtsov introduced the theory of soft sets, which canbe seen as a new mathematical approach to vagueness. The main goal of thispaper is to introduce and study some classes of ordered semihypergroups andto investigate some interesting characterizations theorems of these classesin terms of int-soft hyperideals. In this respect, we characterize weaklyregular ordered semihypergroups for example (see Theorems 25, 26 and 28)intra-regular and left weakly-regular ordered semihypergroups (see Theorems30 and 32) and semisimple ordered semihypergroups (see Theorems 37 and 39)in terms of int-soft hyperideals. In this regard, we study semisimpleordered semihypergroups and characterize it in terms of int-softhyperideals. We also characterize intra-regular and weakly-regular orderedsemihypergroups in terms of int-soft hyperideals
Gregus type fixed point theorems for weakly subsequentially continuous mappings satisfying strict contractive condition of integral type
Full text linkIn the present paper, we prove two common fixed point theorems of Gregus type for two pairs of self mappings satisfying strict contractive condition of integral type by using the weak subsequential continuity property with compatibility of type due to Singh and Mishra [Coincidence and fixed points of reciprocally continuous and compatible hybrid maps, Internat. J. Math. Math. Sci. 10 (2002), 627-635] in metric spaces. Our results improve and the results of Chauhan et al. [Some integral type fixed-point theorems and an application to systems of functional equations, Vietnam J. Math. 42 (2014), no. 1, 17-37] and relevant literature
Subordination properties of certain subclasses of p-valent functions defined by an integral operator
Full text linkIn this paper, we investigate inclusion relationships among certain classes of p-valent analytic functions which are defined by means of integral operator
Atomic and nonatomic Operator-Valued Measures in Locally Convex Cones
Full text linkThe operator valued measures and integrals for cone-valued functions have been investigated in [W. Roth, Operator-valued measures and integrals for cone-valued functions, Lecture Notes in Mathematics, vol. 1964, 2009, Springer Verlag, Heidelberg-Berlin-New York]. In this paper, we define atomic and nonatomic operator valued measures in locally convex cones and investigate their properties. We prove that every operator valued measure can be written as the sum of an atomic and a nonatomic measures
Strong Full Exceptional Collections on Certain Toric Varieties with Picard Number Three via Mutations
Full text linkIn this paper, we study the derived category of certain toric va- rieties with Picaed number three which are blowing-up another toric varieties along their torus invariant loci of codimension at most three. We construct strong full exceptional collections by using Orlov’s blow-up formula and mu- tations. 
On the minimal submodules of a module
Full text linkFor any module over a commutative ring , (resp. ) is the collection of all second (resp. minimal) submodules of . In this article we investigate the interplay between the topological properties of and module theoretic properties of . Also, for various types of modules , we obtain some conditions under which is homeomorphic with the maximal ideal space of some ring
Weighted composition operator valued integral
Full text linkIn the paper we are going to introduce a weighted composition operator-valued integral on L2(X) with a weakly integrable weight function u and we will consider some classic properties of these kind operators.Then we will give the necessary and sufficienti conditions for uniqueness dual pair of