Sahand Communications in Mathematical Analysis
Volume:2 Issue: 2, Summer-Autumn 2015

In this paper, we introduce the notion of generalized multivalued F- weak contraction and we prove some fixed point theorems related to introduced contraction for multivalued mapping in complete metric spaces. Our results extend and improve the results announced by many others with less hypothesis. Also, we give some illustrative examples.

In this paper, a new class of fuzzy sets called fuzzy strongly g∗-closed sets is introduced and its properties are investigated. Moreover, we study some more properties of this type of closed spaces.

This article presents a unified approach to the abstract notions of partial convolution and involution in Lp-function spaces over semi-direct product of locally compact groups. Let H and K be locally compact groups and τ:H→Aut(K) be a continuous homomorphism. Let Gτ=H⋉τK be the semi-direct product of HH and KK with respect to τ. We define left and right τ-convolution on L1(Gτ) and we show that, with respect to each of them, the function space L1(Gτ) is a Banach algebra. We define τ-convolution as a linear combination of the left and right τ -convolution and we show that the τ-convolution is commutative if and only if K is abelian. We prove that there is a τ-involution on L1(Gτ) such that with respect to the τ-involution and ττ-convolution, L1(Gτ) is a non-associative Banach ∗-algebra. It is also shown that when K is abelian, the τ-involution and τ-convolution make L1(Gτ) into a Jordan Banach ∗-algebra. Finally, we also present the generalized notation of τ-convolution for other Lp-spaces with p>0

A generalization of Schauder basis associated with the concept of generalized analytic functions is introduced. Corresponding concepts of density, completeness, biorthogonality and basicity are defined. Also, corresponding concept of the space of coefficients is introduced. Under certain conditions for the corresponding operators, some properties of the space of coefficients and basicity criterion are considered.

In 2004, Rodr''{i}guez-Lallena and ''{U}beda-Flores have introduced a class of bivariate copulas which generalizes some known families such as the Farlie-Gumbel-Morgenstern distributions. In 2006, Dolati and ''{U}beda-Flores presented multivariate generalizations of this class. Then in 2011, Kim et al. generalized Rodr''{i}guez-Lallena and ''{U}beda-Flores'' study to any given copula family. But there are some inaccuracies in the study by Kim et al. We mean to consider the interval for the parameter proposed by Kim et al. and show that it is inaccurate.

In this paper we prove existence the common fixed point with different conditions for α−ψ-contractive mappings. And generalize weakly Zamfirescu map in to modified weakly Zamfirescu map.

In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.8. Chaotic dynamics and synchronization of fractional order PMSM systemIn this paper, we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor (PMSM) system. The necessary condition for the existence of chaos in the fractional-order PMSM system is deduced and an active controller is developed based on the stability theory for fractional systems. The presented control scheme is simple and flexible, and it is suitable both for design and for implementation in practice. Simulation is carried out to verify that the obtained scheme is efficient and robust for controlling the fractional-order PMSM system.

In this paper, we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor (PMSM) system. The necessary condition for the existence of chaos in the fractional-order PMSM system is deduced and an active controller is developed based on the stability theory for fractional systems. The presented control scheme is simple and flexible, and it is suitable both for design and for implementation in practice. Simulation is carried out to verify that the obtained scheme is efficient and robust for controlling the fractional-order PMSM system.