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M. Eshaghi Gordji

Publications and source records attributed to M. Eshaghi Gordji.

At least 19 recordsLinked to original sources

Altered structural balance of resting-state networks in autism

What makes a network complex, in addition to its size, is the interconnected interactions between elements, disruption of which inevitably results in dysfunction. Likewise, the brain networks' complexity arises from interactions beyond pair connections, as it is simplistic to assume that in complex networks state of a link is independently determined only according to its two constituting nodes. This is particularly of note in genetically complex brain impairments, such as the autism spectrum disorder (ASD), which has a surprising heterogeneity in manifestations with no clear-cut neuropathology. Accordingly, structural balance theory (SBT) affirms that in real-world signed networks, a link is remarkably influenced by each of its two nodes' interactions with the third node within a triadic interrelationship. Thus, it is plausible to ask whether ASD is associated with altered structural balance resulting from atypical triadic interactions. In other words, it is the abnormal interplay of positive and negative interactions that matters in ASD, besides and beyond hypo (hyper) pair connectivity. To address this question, we explore triadic interactions based on SBT in the weighted signed resting-state functional magnetic resonance imaging networks of participants with ASD relative to healthy controls (CON). We demonstrate that balanced triads are overrepresented in the ASD and CON networks while unbalanced triads are underrepresented, providing first-time empirical evidence for the strong notion of structural balance on the brain networks. We further analyze the frequency and energy distributions of different triads and suggest an alternative description for the reduced functional integration and segregation in the ASD brain networks. Moreover, results reveal that the scale of change in the whole-brain networks' energy is more narrow in the ASD networks during development.

q-bio.NC↗

A Model as a Repeated Partnership Game with Discounting

In this paper, we present a model of Partnership Game with respect to the important role of partnership and cooperation in nowdays life. Since such interactions are repeated frequently, we study this model as a Stage Game in the structure of infinitely repeated games with a discount factor $δ$ and Trigger strategy. We calculate and compare the payoffs of cooperation and violation and as an important result of this study, we show that each partner will adhere to the cooperation.

math.DS↗

An extension of Mizoguchi-Takahaashi's fixed point theorem

Our main theorem is an extension of the well-known Mizoguchi-Takahaashi's fixed point theorem [N. Mizogochi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, {\it J. Math. Anal. Appl.} 141 (1989) 177--188].

math.MG↗

Cone Normed Spaces

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

math.FA↗

Approximately Lie ternary $(σ,τ,ξ)-$derivations on Banach ternary algebras

Let $A$ be a Banach ternary algebra over a scalar field $\Bbb R$ or $\Bbb C$ and $X$ be a ternary Banach $A-$module. Let $σ,τ$ and $ξ$ be linear mappings on $A$, a linear mapping $D:(A,[]_A)\to (X,[]_X)$ is called a Lie ternary $(σ,τ,ξ)-$derivation, if $$D([abc]_A)=[[D(a)bc]_X]_{(σ,τ,ξ)}+[[D(b)ac]_X]_{(σ,τ,ξ)}+[[D(c)ba]_X]_{(σ,τ,ξ)},$$ for all $a,b,c\in A$, where $[abc]_{(σ,τ,ξ)}=aτ(b)ξ(c)-σ(c)τ(b)a.$ In this paper, we investigate the generalized Hyers--Ulam--Rassias stability of Lie ternary $(σ,τ,ξ)-$derivations on Banach ternary algebras.

math.FA↗

Jordan $*-$homomorphisms between unital $C^*-$algebras

Let $A,B$ be two unital $C^*-$algebras. We prove that every almost unital almost linear mapping $h:A\longrightarrow B$ which satisfies $h(3^nuy+3^nyu) = h(3^nu)h(y)+h(y)h(3^nu)$ for all $u\in U(A)$, all $y\in A$, and all $n = 0, 1, 2,...$, is a Jordan homomorphism. Also, for a unital $C^*-$algebra $A$ of real rank zero, every almost unital almost linear continuous mapping $h:A\longrightarrow B$ is a Jordan homomorphism when $h(3^nuy+3^nyu) = h(3^nu)h(y)+h(y)h(3^nu)$ holds for all $u\in I_1(A_{sa})$, all $y\in A,$ and all $n = 0, 1, 2,... ~$. Furthermore, we investigate the Hyers--Ulam--Rassias stability of Jordan $*-$homomorphisms between unital $C^*-$algebras by using the fixed points methods.

math.OA↗

On certain classes of harmonic functions defined by the fractional derivatives

In this paper we have introduced two new classes $\mathcal{H}\mathcal{M}(β, λ, k, ν)$ and $\overline{\mathcal{H}\mathcal{M}} (β, λ, k, ν)$ of complex valued harmonic multivalent functions of the form $f = h + \overline g$, satisfying the condition \[ Re \{(1 - λ) \frac{Ω^vf}{z} + λ(1-k) \frac{(Ω^vf)'}{z'} + λk \frac{(Ω^vf)''}{z''} \} > β, (z\in \mathcal{D})\] where $h$ and $g$ are analytic in the unit disk $\mathcal{D} = \{z : |z| < 1\}.$ A sufficient coefficient condition for this function in the class $\mathcal{H}\mathcal{M}(β, λ, k, ν)$ and a necessary and sufficient coefficient condition for the function $f$ in the class $\overline{\mathcal{H}\mathcal{M}}(β, λ, k, ν)$ are determined. We investigate inclusion relations, distortion theorem, extreme points, convex combination and other interesting properties for these families of harmonic functions.

math.CV↗

Inequalities for the Polar Derivative of a Polynomial

In this paper we obtain new results concerning maximum modulus of the polar derivative of a polynomial with restricted zeros. Our results generalize and refine upon the results of Aziz and Shah [An integral mean estimate for polynomial, Indian J. Pure Appl. Math. 28 (1997) 1413--1419] and Gardner, Govil and Weems [Some result concerning rate of growth of polynomials, East J. Apporox. 10(2004) 301--312].

math.CV↗

On the stability of J$^*-$derivations

In this paper, we establish the stability and superstability of $J^*-$derivations in $J^*-$algebras for the generalized Jensen--type functional equation $$rf(\frac{x+y}{r})+rf(\frac{x-y}{r})= 2f(x).$$ Finally, we investigate the stability of $J^*-$derivations by using the fixed point alternative.

math.FA↗

Stability of $(α,β,γ)-$derivations on Lie $C^*-$algebras

Petr Novotný and Jiřĺ Hrivnák \cite{Nov} investigated generalize the concept of Lie derivations via certain complex parameters and obtained various Lie and Jordan operator algebras as well as two one- parametric sets of linear operators. Moreover, they established the structure and properties of $(α,β,γ)-$derivations of Lie algebras. We say a functional equation $(ξ)$ is stable if any function $g$ satisfying the equation $(ξ)$ {\it approximately} is near to true solution of $(ξ).$ In the present paper, we investigate the stability of $(α,β,γ)-$derivations on Lie $C^*$-algebras associated with the following functional equation $$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3 x_3}{3})+ f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$ }

math.DG↗

On systems of nonlinear equations

In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.

math.DS↗

Quadratic--quartic functional equations in RN--spaces

In this paper, we obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary $t$-norms $$f(2x+y)+f(2x-y)=4[f(x+y)+f(x-y)]+2[f(2x)-4f(x)]-6f(y).$$

math.FA↗