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Open Access Article
1 - A new subclass of harmonic mappings with positive coefficients
A. R. Haghighi N. Asghary A. Sedghi‎Complex-valued harmonic functions that are univalent and‎‎sense-preserving in the open unit disk $U$ can be written as form‎‎$f =h+\bar{g}$‎, ‎where $h$ and $g$ are analytic in $U$‎.‎In this paper‎, ‎we introduce the class $S More‎Complex-valued harmonic functions that are univalent and‎‎sense-preserving in the open unit disk $U$ can be written as form‎‎$f =h+\bar{g}$‎, ‎where $h$ and $g$ are analytic in $U$‎.‎In this paper‎, ‎we introduce the class $S_H^1(\beta)$‎, ‎where $1<\beta\leq 2$‎, ‎and‎‎consisting of harmonic univalent function $f = h+\bar{g}$‎, ‎where $h$ and $g$ are in the form‎‎$h(z) = z+\sum\limits_{n=2}^\infty |a_n|z^n‎$ ‎and ‎‎$‎g(z) =‎\sum\limits_{n=2}^\infty |b_n|\bar z^n$‎for which‎‎$$\mathrm{Re}\left\{z^2(h''(z)+g''(z))‎ +2z(h'(z)+g'(z))-(h(z)+g(z))-(z-1)\right\}<\beta.$$‎It is shown that the members of this class are convex and starlike‎.‎We obtain distortions bounds extreme point for functions belonging to this class‎,‎and we also show this class is closed under‎convolution and convex combinations‎. Manuscript profile -
Open Access Article
2 - Invariant elements in the dual Steenrod algebra
T. Vergili I. Karaca‎In this paper‎, ‎we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${\mathcal{A}_p}^*$ under the conjugation map $\chi$ and give bounds on the dimensions of $(\chi-1)({\mathcal{A}_p}^*)_d$‎, ‎where $({\mathcal{A}_p}^*)_d$ More‎In this paper‎, ‎we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${\mathcal{A}_p}^*$ under the conjugation map $\chi$ and give bounds on the dimensions of $(\chi-1)({\mathcal{A}_p}^*)_d$‎, ‎where $({\mathcal{A}_p}^*)_d$ is the dimension of ${\mathcal{A}_p}^*$ in degree $d$‎. Manuscript profile -
Open Access Article
3 - $(F,\varphi ,\alpha )_{s}$-contractions in $b$-metric spaces and applications
M. Sangurlu Sezen‎In this paper‎, ‎we introduce more general contractions called $\varphi $-fixed‎‎point point for $(F,\varphi‎ ,‎\alpha )_{s}$ and $(F,\varphi‎ ,‎\alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of More‎In this paper‎, ‎we introduce more general contractions called $\varphi $-fixed‎‎point point for $(F,\varphi‎ ,‎\alpha )_{s}$ and $(F,\varphi‎ ,‎\alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of $\varphi $-‎fixed point point for $(F,\varphi‎ ,‎\alpha )_{s}$ and $(F,\varphi‎ ,‎\alpha‎‎)_{s}$-weak contractions in complete $b$-metric spaces‎. ‎Some examples are‎‎supplied to support the usability of our results‎. ‎As applications‎, ‎necessary‎‎conditions to ensure the existence of a unique solution for a nonlinear‎‎inequality problem are also discussed‎. ‎Also‎, ‎some new fixed point results in‎‎partial metric spaces are proved. Manuscript profile -
Open Access Article
4 - Application of DJ method to Ito stochastic differential equations
H. Deilami Azodi‎This paper develops iterative method described by [V‎. ‎Daftardar-Gejji‎, ‎H‎. ‎Jafari‎, ‎An iterative method for solving nonlinear functional equations‎, ‎J‎. ‎Math‎. ‎Anal‎. ‎Appl‎. ‎316 (200 More‎This paper develops iterative method described by [V‎. ‎Daftardar-Gejji‎, ‎H‎. ‎Jafari‎, ‎An iterative method for solving nonlinear functional equations‎, ‎J‎. ‎Math‎. ‎Anal‎. ‎Appl‎. ‎316 (2006) 753-763] to solve Ito stochastic differential equations‎. ‎The convergence of the method for Ito stochastic differential equations is assessed‎. ‎To verify efficiency of method‎, ‎some examples are expressed‎. Manuscript profile -
Open Access Article
5 - Ring endomorphisms with nil-shifting property
C. A. K. Ahmed R. T. M. SalimCohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,b\in R.$ The reversible property is an important role in noncommutative ring theory‎. ‎Recently‎, ‎Abdul-Jabbar et al‎. ‎studied the reversible ring property on nilpo MoreCohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,b\in R.$ The reversible property is an important role in noncommutative ring theory‎. ‎Recently‎, ‎Abdul-Jabbar et al‎. ‎studied the reversible ring property on nilpotent elements‎, ‎introducing‎the concept of commutativity of nilpotent elements at zero (simply‎, ‎a CNZ ring)‎. ‎In this paper‎, ‎we extend the CNZ property of a ring as follows‎: ‎Let $R$ be a ring and $\alpha$ an endomorphism of $R$‎, ‎we say that $ R $ is right (resp.‎, ‎left) $\alpha$-nil-shifting ring if whenever $ a\alpha(b) = 0 $ (resp.‎, ‎$\alpha(a)b = 0$) for nilpotents $a,b$ in $R$‎, ‎$ b\alpha(a) = 0 $ (resp.‎, ‎$ \alpha(b)a= 0) $‎. ‎The characterization of $\alpha$-nil-shifting rings and their related properties are investigated‎. Manuscript profile -
Open Access Article
6 - 2n-Weak module amenability of semigroup algebras
K. Fallahi H. Ghahramani‎Let $S$ be an inverse semigroup with the set of idempotents $E$‎.We prove that the semigroup algebra $\ell^{1}(S)$ is always‎‎$2n$-weakly module amenable as an $\ell^{1}(E)$-module‎, ‎for any‎‎$n\in \mathbb{N}$‎, ‎where $E$ acts More‎Let $S$ be an inverse semigroup with the set of idempotents $E$‎.We prove that the semigroup algebra $\ell^{1}(S)$ is always‎‎$2n$-weakly module amenable as an $\ell^{1}(E)$-module‎, ‎for any‎‎$n\in \mathbb{N}$‎, ‎where $E$ acts on $S$ trivially from the left‎‎and by multiplication from the right‎. ‎Our proof is based on a common fixed point property for semigroups‎. Manuscript profile -
Open Access Article
7 - On the square root of quadratic matrices
A. ZardadiHere we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2\times 2$ matrices.Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2\times 2$ matrices. Manuscript profile
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