modular $p$
در نشریات گروه ریاضی-
In the present article, duals, approximate duals and pseudo-duals (generated by bounded and not necessarily adjointable operators) of a frame in a Hilbert $C^\ast$-module are characterized and some of their properties are obtained. Especially, the ones constructed by multiplication operators are discussed and their stability under the action of morphisms is focused and some equivalent conditions for the stability are derived. Finally, we get some results on pseudo-duals of modular Riesz bases, mainly their preservation under the action of morphisms and their behavior in the presence of semi-normalized symbols are studied.Keywords: Hilbert C*-Module, Frame, Dual, Approximate Dual, Pseudo-Dual, Modular Riesz Basis
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International Journal Of Nonlinear Analysis And Applications, Volume:15 Issue: 11, Nov 2024, PP 319 -332This article is a revision and correction of the chapter book [S. Hadi Bonab, V. Parvaneh, Z. Bagheri, $\eta_{\mathcal{A}}$-Admissible Mappings for Four Maps in $C*$-Algebra-Valued MP-Metric Spaces with an Application, In: P. Debnath, Delfim F. M. Torres, Yeol Je Cho, Advanced Mathematical Analysis and its Applications, CRC Press, 2023, 97-113.]. In this article, we first introduce the concept of $\eta$-admissible mapping in $C^*$-algebra valued $\mathcal{MP}$-metric spaces, which is a generalization and combination of "modular metric spaces", "parametric metric spaces" and "$C^*$-algebra-valued metric spaces". Then, for four mappings in these spaces, we prove several fixed-point theorems. We give an example and an application regarding the solvability of operator equations and integral equations, respectively, to support the new findings.Keywords: Metric Space, Parametric Metric Space, Modular Metric Space, $, Eta$-Admissible Mappings, $C^*$-Algebra-Valued Metric Space, $C^*$-Algebra-Valued $, Mathcal{MP}$-Metric Space
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Complementary pairs of symmetric $2$-designs are equivalent to coherent configurations of type $(2, 2; 2)$.D. G. Higman studied these coherent configurations and adjacency algebras of coherent configurations over a field of characteristic zero. These are always semisimple. We investigate these algebras over fields of any characteristic prime and the structures.Keywords: Coherent Configuration, Symmetric Design, P-Rank, Modular Adjacency Algebra, Modular Standard Module
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Journal of Mathematical Analysis and its Contemporary Applications, Volume:6 Issue: 2, Spring 2024, PP 71 -91In this paper, we define the notions of Ξ-conditionally commuting, Ξ-conditionally compatible, Ξ-faintly compatible mappings and Ξ-reciprocal continuous mappings in the setting of modular metric spaces and then prove common fixed point theorems for these mappings. In fact, our results are the generalization of the results of [2], [13] and [18].Keywords: Modular Metric Spaces, Ξ-Non-Compatible, Ξ-Reciprocally Continuous, Ξ-Conditionally Commuting, Ξ-Conditionally Compatible, Ξ-Faintly Compatible Mappings
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 9, Sep 2023, PP 273 -282In this paper, we prove some fixed point theorems for modular metric spaces endowed with partial order sets by using the mixed monotone mapping property which is a generalization of the definitions and results of T. Gnana Bhaskar and V. Lakshmikantham.Keywords: Coupled fixed point, Modular metric spaces, Partially ordered sets
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Abstract. In this paper we introduce the concept of probability of normality of chains in finite groups. For any normal subgroup N of a finite group G, the relation between the probability of normality of chains of G and of its factor group G/N are obtained.Finally, we give explicit formulas for such probability of dihedral groups D_2n, quasi-dihedral groups QD_2n, generalized quaternion groups Q_2n, and the modular p-groups M_p^n.
Keywords: Probability of normality, Dihedral groups, Generalized quaternion groups, Modular p-groups -
In this paper, we present some fixed point results for cyclic weak $\phi$-contractions in $\omega$-complete modular metric spaces and $\omega$-compact modular metric spaces, respectively. Some results for contractions that have zero cyclic properties are also provided.Keywords: modular metric space, fixed point, cyclic $, phi$-contraction, convex modular
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 1, Jan 2023, PP 1825 -1833In this paper, introduced a new accelerated iterative algorithm in \((\lambda,\rho )\) -quasi firmly nonexpansive multi-valued mappings in modular function spaces and present some results for convergence to a fixed point in this mapping, we use faster convergence theorem to comparison our iteration with some other iterations and introduced numerical example. As an application, we have referred to previous work by other researchers.Keywords: Multivalued mappings, quasi firmly nonexpansive mappings, modular function spaces, iterative scheme, Fixed point
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This article aims to characterize a new class of simulation functions by extending the class of $\mathcal{Z}$ functions demonstrated by Cho in \cite{ze}, and via this novel notion, to establish some common fixed point theorems in modular $b-$metric spaces. Furthermore, some corollaries, which enlarge previously existing literature, have been procured. In conclusion, an example and an application to the nonlinear integral equations have been presented to state the applicability and validity of our outcomes.
Keywords: simulation functions, modular b−metricspace, almost contraction -
اگر چه قضایای نقطه ثابت در فضای مدولار، دارای کاربرد قابل توجهی در بخش وسیعی از مسایل ریاضی هستند، این قضایا به طور قوی وابسته به فرضیاتی هستند که اغلب در مسایل کاربردی، یا عملی نیستند و یا تعمیم واقعی از قضایای نقطه ثابت فضای برداری نرمدار نیستند. در تحقیقات اخیر تمرکز بر قضایای نقطه ثابت بنیادی همراه با حذف این فرضیات شده است. در واقع در بخش وسیعی از این تحقیقات در فضای مدولار، فرض کرانداری تابع حذف شده است. فرض محدب بودن مدولار نیز باعث القای نرم می شود و منجر به تبدیل شدن فضای مدولار به فضای نرمدار می گردد از اینرو حذف این شرط نیز باعث اثبات قضایایی جدید و قوی بر فضای مدولار می گردد. اما چنانچه می دانیم اکثر قضایای نقطه ثابت بر فضای مدولار محدب اثبات شده اند.در این مقاله، تعریف فضای شبه مدولار را که در واقع تعمیمی از فضای مدولار است را ارایه می دهیم. و قضایای نقطه ی ثابت تقاطع نگاشت های تعمیم انقباضی ضعیف بر این فضا را اثبات می کنیم. قابل ذکر است که قضایای اثبات شده در اینجا، بدون فرض کرانداری تابع و فرض تحدب شبه مدولار است. از اینرو نتایج به دست آمده در این مقاله، قضایای نقطه ثابت را در چند وجه تعمیم می دهند. همچنین ما دو مثال می آوریم و به کمک قضایای اثبات شده در این مقاله وجود نقطه ثابت را نشان دهیم. علاوه بر این، بعنوان کاربرد، وجود جواب برای دستگاه خاصی از معادلات انتگرالی را به کمک نتایج اصلی نشان می دهیم.
کلید واژگان: نقطه ثابت مشترک، فضای شبه مدولار، نگاشت های انقباضی به طور ضعیف تعمیم یافتهAlthough fixed point theorems in modular spaces have remarkably applied to a wide variety of mathematical problems, these theorems strongly depend on some assumptions which often do not hold in practice or can lead to their reformulations as particular problems in normed vector spaces. A recent trend of research has been dedicated to studying the fundamentals of fixed point theorems and relaxing their assumptions with the ambition of pushing the boundaries of fixed point theory in modular spaces further. The convexity is an assumption which lead to converting of modular space to the normed space so relaxing this assumption lead to stronger theorems. But as we know much theorems are proved on convex modular spaces.In this paper, we introduce the modular-like definition which is a generalization of modular space. And common fixed point of generalized weakly contraction mappings are proved. We focus on convexity and boundedness of modular-like in fixed point results taken from the literature for generalized weakly contractive mappings. So our results, generalized fixed point theorems in many acpects. Afterwards we present examples and an application to a particular form of integral inclusions to support our main results.
Keywords: Common fixed point, Modular-like space, generalized weakly contraction mappings -
Journal of Mathematical Analysis and its Contemporary Applications, Volume:4 Issue: 1, Winter 2022, PP 53 -70The aim of this paper is to prove a common fixed point theorem for two pairs of $omega$-compatible and $omega$-weakly compatible maps for extending and generalizing the results of Murthy and Prasad [12] in modular metric spaces. The main result is also illustrated by an example to demonstrate the degree of validity of our hypothesis.Keywords: Common fixed point, $emptyset$-Weak Contraction, Modular Metric Spaces, $omega-$compatible map, $omega-$weakly Compatible map
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In this paper we introduce `omega`-proximal quasi contraction mapping and best `omega`-proximity point in modular metric spaces. In fact, we show that
every `omega`-proximal quasi contraction mapping has unique best `omega`-proximity point in modular metric spaces. Finally, we give an example to illustrate the applications of our results.Keywords: modular metric space, best proximity point, proximal quasi contraction map, $omega$-proximal quasi contraction, proximal Picard sequence, T-orbitally $omega$-complete -
The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.
Keywords: Fixed point, Weak contraction, Partially ordered space, Modular metric space -
هدف اصلی این مقاله حل دستگاه های معادلات همنهشتی خطی روی CF-حلقه های جابجایی می باشد. فرض کنید R یک CF-حلقه و I_1, …, I_n ایده آلهایی از این حلقه باشند. در این مقاله روش های حل یک دستگاه معادلات خطی همنهشتی به پیمانه این ایده آلها را مطالعه میکنیم. در این راستا، تکنیک هایی از نظریه ماتریس های همنهشتی را معرفی می کنیم و به عنوان کاربردی از این تکنیک ها به حل دستگاه بالا می پردازیم. در پایان کاربردی از تکنیک های جبر محاسباتی (پایه های گربنر) در این زمینه در حالت خاص R=Z را مورد بررسی قرار می دهیم.کلید واژگان: دستگاه های همنهشتی خطی، عملیات حذفی گاوسی، پایه های گربنرIn this paper, we deal with solving systems of linear congruences over commutative CF-rings. More precisely, let R be a CF-ring (every finitely generated direct sum of cyclic R-modules has a canonical form) and let I_1,..., I_n be n ideals of R. We introduce congruence matrices theory techniques and exploit its application to solve the above system. Further, we investigate the application of computer algebra techniques (Gröbner bases) in this context whenever R = Z.Keywords: Linear congruence systems, Modular Gaussian elimination, Grobner bases
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Some functional inequalitiesý ýin variable exponent Lebesgue spaces are presentedý. ýThe bi-weighted modular inequality with variable exponent p(.) for the Hardy operator restricted to noný- ýincreasing function which isý
ýýinti0nfty(frac1xintx0f(t)dt)p(x)v(x)dxleqýýCinti0nftyf(x)p(x)u(x)dxý,ý
ýýis studiedý. ýWe show that the exponent p(.) for which these modular inequalities hold must have constant oscillationý. ýAlso we study the boundedness of integral operator Tf(x)=intK(x,y)f(x)dy on Lp(.) when the variable exponent p(.) satisfies someý ýuniform continuity condition that is named beta -controller condition and so multiple interesting results which can beý ýseen as a generalization of the same classical results in the constant exponent caseý, ýderivedý.Keywords: Hardy type inequality, Variable exponent Lebesgue space, Modular type inequality -
In this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. Explicit formulas are given for dihedral groups $D_{2n}$, quasi-dihedral groups $QD_{2^n}$, generalized quaternion groups $Q_{4n}$ and modular $p$-groups $M_{p^n}$.Keywords: Fuzzy subgroup, Dihedral group, Generalized quaternion group, Quasi, dihedral $2$, group, Modular $p$, group
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A modular $k$-coloring, $kge 2,$ of a graph $G$ without isolated vertices is a coloring of the vertices of $G$ with the elements in $mathbb{Z}_k$ having the property that for every two adjacent vertices of $G,$ the sums of the colors of the neighbors are different in $mathbb{Z}_k.$ The minimum $k$ for which $G$ has a modular $k-$coloring is the modular chromatic number of $G.$ Except for some special cases modular chromatic number of $C_msquare P_n$ is determined.Keywords: modular coloring, modular chromatic number, Cartesian product
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