Journal of Mahani Mathematical Research
Volume:10 Issue: 1, Winter and Spring 2021

‎We show that a nonautonomous discrete-time dynamical system (NDS) with the ergodic shadowing property is chain mixing‎. ‎As a result‎, ‎it is obtained that a $ k $-periodic NDS with the ergodic shadowing property has the shadowing property‎. In particular‎, ‎any $ k $-periodic NDS on intervals having the ergodic shadowing is Devaney chaotic‎. Additionally‎, ‎we prove that for an equicontinuous NDS with the shadowing property‎, ‎the notions of topologically mixing‎, ‎pseudo-orbital specification‎, ‎weak specification property‎, ‎and ergodic shadowing property are equivalent‎.

For the function f(z) analytic in the open unit disk and normalized by f(0) = f0(0)−1 = 0, we consider the expression; ( zf0(z)f(z)−1)+1−( zf(z) );( > 0). Using differential subordination notion, we investigate properties of ( f(z) z ), as well as, sufficient conditions for univalence and starlikeness of f(z). In the special case, for  = 1, these results generalize and improve some previously results given in the literature.

In this paper, we study the properties of some classes of quotientorder-homomorphisms, as product stable in the category of topological fuzzes.We dene the concept of a bi-quotient order-homomorphism and show that forHausdorff topological fuzzes, a quotient order-homomorphism f : L1 ! L2 isproduct stable if and only if f is bi-quotient and L2 is a core compact topologicalfuzz.

In this study, the concept of an inverse matrix including fuzzy number elements is extended. Such a concept may be performed in the modeling of uncertain and imprecise real-world problems. The problem of finding a fuzzy inverse matrix is converted to a problem to solve a system of fuzzy polynomial equations. Here, a fuzzy system is transformed to an equivalent system of crisp polynomial equations. The solution of the system of crisp polynomial equations is calculated using Wu’s method and is introduced a criterion for invertibility of a fuzzy matrix (FM). In addition, an algorithm is proposed to calculate the fuzzy inverse matrix. The most important advantage of the presented method is that it achieves whole inverse entries of an FM, simultaneously. In the end, we give some illustrative examples to show the efficiency and proficiency of our proposed algorithm.

In recently years, frames in Krein spaces had been considered. The paper presents a family of generators for a Krein space by their frames. These generators are dual frames and operator dual frames corresponding to a given frame in a Krein space. We characterize all generalized dual frames of a primary frame. Also, approximately dual frames in a Krein space are introduced and, we study the relation between approximately dual frames and operator duals in a Krein space. Finally, perturbation of frames in this space is considered.

In this paper we classify proper $L_k$-biharmonic hypersurfaces $ M $, in the unit Euclidean sphere which has two principal curvatures and we show that they are open pieces of standard products of spheres. Also we study proper $L_k$-biharmonic compact hypersurfaces $ M $ with respect to $tr(S^2circ P_k)$ and $ H_k $ where $ S $ is the shape operator, $ P_k $ is the Newton transformation and $ H_k $ is the $ k $-th mean curvature of $ M $, and by definiteness's assumption of $ P_k $, we show that $ H_{k+1} $ is constant.

This paper investigates the existence and interval of existence, uniqueness and Ulam stability of solutions on initial value type problem of a nonlinear Caputo fractional Volterra-Fredholm integro-differential equation in Banach spaces.

In this paper, we give some distance formulas for 3-dimensional maximum space. We study in 3-dimensional analytical space furnishing with maximum metric, and in this space we give distance formulas between a point and a line, a point and a plane and between two lines in terms of maximum metric.

Let F denote a specific space of the class of was costructed by H. Khodabakhshian as a classes of separable Banach function spaces analogous to the james function spaces. In this notes we prove that l_p(α) is isomorphic to a complemented subspace of F_{α,p} and for p = 2, F_{α,p} is a closed subspace of the Waterman-Shiba space αBV^ (p) Assume F denotes a specific space of the class of F_{α,p} that was costructed by H. Khodabakhshian[2] as a classes of separable Banach function spaces analogous to the James function spaces. In this notes we prove that l_p(α) is isomorphic to a complemented subspace of F_{α,p} and for p = 2, F_{α,p} is a closed subspace of Waterman-Shiba space αBV^(p).

In this paper, we consider “Nearest points” and “Farthest points” in inner product spaces and Hilbert spaces. The convexity of Chebyshev sets in Hilbert spacse is an open problem. In this paper we define sun sets and sunrise sets in normed spaces.

ABSTRAct. In this paper, a relative intuitionistic dynamical system with the levels (α, β), as a mathematical model compatible with a natural phenome- non, is proposed. In addition, the notion of RI topological entropy with the levels (α, β) for RI dynamical systems with the levels (α, β) is defined and its properties are studied. As a significant result, it was shown that, this topolog- ical entropy is an invariant object up to conjugate relation.

In this paper, by using SOR-Like method that introduced by Golub, Wu and Yuan and generalized Taylor expansion method for solving linear systems [F.Toutounian, H. Nasabzadeh, A new method based on the generalized Taylor expansion for computing a series solution of linear systems, Appl. Math. Comput. 248 (2014) 602-609], the GTSOR-Like method is proposed for augmented systems. The convergence analysis and the choice of the parameters of the new method are discussed. While there is no guarantee the SOR-Like method converges for the negative parameter, ω additional parameters of the new method can be adjusted for the corresponding GTSOR-Like method to converge. Finally, numerical examples are given to show that the new method is much more efficient than the SOR-Like method.