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s-$function

در نشریات گروه ریاضی
تکرار جستجوی کلیدواژه s-$function در نشریات گروه علوم پایه
  • Abolfazl Tari, Sedaghat Shahmorad *, Mahdi Mostafazadeh, Fevzi Erdogan
    The aim of this paper is to solve a class of  auto-convolution Volterra integral equations by the well-known differential transform method. The analytic property of solution and convergence of the method under some assumptions are discussed and some illustrative examples are given to clarify the theoretical results, accuracy and performance of the proposed method.
    Keywords: Volterra Integral Equations, Auto-Convolution, Differential Transform Method, Analytic Function
  • Parisa Hasanalipour, M. Razmkhah *, G. R. Mohtashami Borzadaran

    The skewed and weighted distributions may be considered as nice alternatives to fit a real data set in practical situations in which the well-known distributions are not suitable. The weighted distributions are first discussed and then two extensions of weighted models are proposed in this paper to analyze the skew data. The flexibility of the models is studied in view of the moment skewness coefficient for some cases. Finally, two real data sets are used to illustrate the results of the paper.

    Keywords: Proportional Hazard Rate Model, Skew Symmetric Distribution, Skewness Coefficient, Weight Function
  • Houria Chellaoua *, Yamna Boukhatem
    In this paper, we consider a general class of nonautonomous abstract delayed evolution equations with a nonlinear source term. Under appropriate assumptions on the time-independent operator and the initial data, we establish global existence using the method of steps and employing classical results from the theory of inhomogeneous evolution problems. Then, by assuming that the operator associated with the non-delayed part of the system generates an exponentially stable semigroup, we obtain an exponential decay estimate. This is achieved through a direct proof based on Duhamel's formula combined with Gronwall's inequality, under Lipschitz continuity conditions on the nonlinear source term. Finally, we conclude the paper by providing illustrative examples that validate the generalized setting of our system.
    Keywords: Duhamel's Formula, Energy Function, Evolutionary Family, Lipschitz Continuous
  • Khatere Sheikhi*, Shahram Najafzadeh

    In the present paper, we introduce and investigate a new result connected to subclasses of normalized and univalent functions in the open unit disk. Some majorization results and geometric properties such as radii of starlikeness, convexity, pre-Schwarzian norm and coefficient estimates are obtained.

    Keywords: Analytic Function, Starlike Function, Subordination
  • Ismail Nikoufar *, Zahra Baghernezhad Shayan

    Some Hilbert $C^*$-module versions of H$\ddot{o}$lder-McCarthy and H$\ddot{o}$lder type inequalities and their complementary on a Hilbert $C^*$-module are obtained by Seo \cite{seo-2014}. The purpose of this paper is to extend these results for some operator convex (resp. concave) functions on a Hilbert $C^*$-module via the operator perspective approach. By choosing some elementary functions, we reach some new types of inequalities in Hilbert $C^*$-modules.

    Keywords: Operator Convex Function, Adjointable Operators, Perspective Function, H$, Ddot{O}$Lder Inequality
  • Artion Kashuri, Muhammad Talha, Soubhagya Sahoo *
    In this paper, new generalized variants of Ostrowski’s type identities involving the Atangana-Baleanu-Katugampola fractional integral operator for differentiable convex and twice differentiable convex functions are presented. Using these equalities or lemmas along with several known identities, new inequalities for convex functions and the Atangana-Baleanu-Katugampola, fractional integral operators are proved. By making appropriate choices of parameters, some connections between our results and various other findings are also recognized in the paper. Finally, some applications to unique means for positive real numbers are offered.
    Keywords: Ostrowski Inequality, Convex Function, Atangana-Baleanu Katugampola Fractional Integral Operator, H, {O}Lder's Inequality, Power-Mean Inequality, Young's Inequality, Special Means, Estimations
  • Gholamreza Hesamian, Mohamadghasem Akbari, Mehdi Shams*

    Multivariate regression is an approach for modeling the linear relationship between several variables. This paper proposed a ridge methodology with a kernel-based weighted absolute error target with exact predictors and fuzzy responses. Some standard goodness-of-fit criteria were also used to examine the performance of the proposed method. The effectiveness of the proposed method was then illustrated through two numerical examples including a simulation study. The effectiveness and advantages of the proposed fuzzy multiple linear regression model were also examined and compared with some well-established methods through some common goodness-of-fit criteria. The numerical results indicated that our prediction/estimation gives more accurate results in cases where multicollinearity and/or outliers occur in the data set.

    Keywords: Goodness-Of-Fit Measure, Robust, Multicollinearity, Kernel Function, Outlier
  • Bilender PAŞAOĞLU ALLAHVERDİEV, Hüseyin TUNA, YÜKSEL YALÇINKAYA *
    In this study, beta-derived Sturm–Liouville problems are discussed. First, the existence and uniqueness problem for such equations is discussed. Then, self-adjointness is obtained with the help of boundary conditions. Eigenfunction expansion was obtained with the help of characteristic determinants and Green’s function. Finally, an example is given showing the theoretical results obtained.
    Keywords: Fractional Differential Equations, Self-Adjoint Operators, Green’S Function, Eigenfunction Expansion
  • Vahid Vesali, Shahram Najafzadeh *

    In this paper, we extend the $q$-derivative operator, which plays an essential role in quantum calculus. Indeed, by using the Hadamard product and generalized Koebe function we define the following $(\alpha,\beta,\gamma)$-derivative operator\begin{equation*}    {\rm d}_{\alpha,\beta,\gamma} f(z)=\frac{1}{z}\left\{f(z)*\mathfrak{L}_{\alpha,\beta,\gamma}(z)\right\},\end{equation*}where\begin{equation*}    \mathfrak{L}_{\alpha,\beta,\gamma}(z)=\frac{2(1-\gamma)z}{(1-\alpha z)(1-\beta z)},\end{equation*}and $\alpha\in[-1,1]$, $\beta\in[-1,1]$, $\alpha\beta\neq \pm1$ and $\gamma\in[0,1)$. Then by subordination relation, the operator ${\rm d}_{\alpha,\beta,\gamma} f(z)$, and a special function $\phi_\delta(z)=1+\delta z/\exp(\delta z)$ ($0<\delta\leq1$), we define a new particular Ma-Minda class. We investigate some properties of this class, such as, radius problem and coefficient estimate.

    Keywords: Unit Disk, Analytic Functions, Starlike Function, Subordination, Radius Problems, Coefficients Problems
  • محمدرضا فریدروحانی*، سکینه دهقان، علی هدایتی

    در این مقاله یک نمودار جدید کنترلی ناپارامتری چندمتغیره در فاز دو بر اساس تابع ژرفا ارائه می شود. آماره پیشنهادی ناوردای آفین و مجانبا آزاد توزیع است. در واقع، توزیع مجانبی آماره پیشنهادی در حالت تحت کنترل بودن فرآیند، حاصل می شود. بر اساس مطالعات شبیه سازی، عملکرد آماره پیشنهادی بر اساس چندین تابع ژرفا محاسبه و با سه آماره رقیب مقایسه شده است. نتایج نشان می دهد که آماره معرفی شده دارای عملکرد قابل قبولی بوده و در برخی حالات بهتر از آماره های رقیب است. بر اساس نمودار پیشنهادی، یک مجموعه داده واقعی مورد تحلیل قرار گرفته است.

    کلید واژگان: نمودارهای کنترل کیفیت چندمتغیره، ناوردای آفین، تابع ژرفا، فاز دو
    Mohammadreza Faridrohani *, Sakineh Dehghan, Ali Hedayati

    This article presents a new multivariate non-parametric control chart in Phase II based on depth functions. The proposed statistic is an affine invariant and asymptotically free distribution. Indeed, the asymptotic distribution of the proposed statistic is derived under the in-control process. Based on simulation studies, the performance of the proposed statistic, using several depth functions, has been evaluated and compared with three competing statistics. The results show that the introduced statistic performs adequately and, in some cases, outperforms the competing statistics. A real dataset has been analyzed based on the proposed chart.

    Keywords: Nonparametric Multivariate Control Chart, Affine Invariant, Depth Function, Phase ІІ
  • Muhammet Kamali *
    We define a class of analytic functions, $A(H, n, m, \lambda)$, satisfying the following condition\begin{equation*}\frac{D_{\lambda}^{n+m} f(z)}{D_{\lambda}^{n} f(z)} \prec H(z, t),\end{equation*}where $\lambda \geq 0,n,m\in \mathbb{N}^{\ast }=\mathbb{N}\cup \{0\},t\in\left( \frac{1}{2},1\right] $ and for all $z\in \Omega $. In this study, firstly give estimates for coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $ of functions belong to this class. Furthermore, the Fekete- Szeg\"{o} inequality was examined for the functions belonging to this class.
    Keywords: Analytic Function, Salagean Operator, Coefficient Estimates, Fekete-Szegö Inequality
  • Nanasaheb Phatangare *, Krishnat Masalkar, Subhash Kendre
    In this paper, we obtained the Poincare return maps for the planar piecewise linear differential systems of the type focus-focus. Normal forms for planar piecewise smooth systems with two zones of the type focus-focus and saddle-saddle, separated by a straight line and with a center at the origin, are obtained. Upper bounds for the number of limit cycles bifurcated from the period annulus of these normal forms due to perturbation by polynomial functions of any degree are established.
    Keywords: Piecewise Linear Differential System, Piecewise Smooth Differential System, Limit Cycle, Picard Fuch Equations, Poincare Return Map, Melnikov Function
  • Monika Bisht, Shivam Rawat *, Junaid Ahmed
    Game theory has significant importance in various domains as it is a powerful tool that helps the rational decision-makers to understand and assess strategic interactions. It develops mathematical models to depict these strategic engagements in competitive environments. Given the inherent uncertainty in real-world problems, obtaining exact values of payoffs for a matrix game can be difficult. In many instances, however, these payoffs vary within certain ranges, which makes in-terval numbers the best form to represent them. This results in the creation of a specialized category of game problem which is referred to as the interval-valued matrix game (IVMG). According to the literature, various methodologies exist to identify the optimal strategies and game value for IVMGs. However, many of these methods possess some shortcomings dis-cussed in the paper, highlighting the requirement for a novel approach. Therefore, in the present study, we propose a novel method to find solutions to game problems with interval payoffs, utilizing the fuzzy concept. Since operations and comparisons on interval numbers are not well-defined, we transform the elements of payoff matrix into a fuzzy represen-tation. Utilizing ranking function for defuzzification of these fuzzy payoffs, we transform them to crisp form. The solu-tion for the subsequent crisp matrix game is obtained using a graphical technique or linear programming problem ap-proach. Additionally, numerical examples are provided for validation of the presented method. The game values for these examples are also obtained using methods presented by other researchers in the literature, and comparisons with these methods are made, highlighting the limitations of the methods in the existing literature and significance of the presented method. Finally, conclusions with shortcomings and future scope of research based on the paper are described.
    Keywords: Generalized Pentagonal Fuzzy Number, Generalized Hexagonal Fuzzy Number, Fuzzification, Ranking Function, Two Person Zero-Sum Game, Value Of Game
  • فاطمه ابطحی*، مریم توتونچی
    فرض کنیم $(\mathcal A,\|\cdot\|_{\mathcal A})$ یک جبر باناخ جابجایی و نیم ساده و $(\mathcal B,\|\cdot\|_{\mathcal B})$ یک جبر سگال مجرد نسبت به $\mathcal A$ باشد. در این مقاله، ابتدا سه نگاشت مهم و کاربردی ${}_{\mathcal A}L$، $\Gamma_1$ و نیز $\Gamma_2$ را یادآوری و مورد مطالعه قرار می دهیم. سپس بررسی می کنیم چه وقت این نگاشت ها دارای برد بسته هستند. در واقع، شرایطی را که بسته بودن برد یکی از این نگاشت ها، بسته بودن برد نگاشت دیگر را نتیجه می دهد، مورد تحقیق و مطالعه قرار می دهیم. بعد از آن با استفاده از این نتایج، یک شرط لازم و کافی ارائه می دهیم برای این که $(\mathcal B,\|\cdot\|_{\mathcal B})$ یک جبر باناخ با نرم BSE باشد. در نهایت، برخی از نتایج عمومی موجود در خصوص جبرهای سگال مجرد وابسته به جبرهای تابعی باناخ طبیعی را برای جبرهای سگال مجرد وابسته به جبرهای باناخ دلخواه تعمیم می دهیم. همچنین در سرتاسر مقاله، مثال های مهمی را برای روشنگری مطالب و نتایج بیان شده، ارائه می دهیم.
    کلید واژگان: تابع، BSE جبر باناخ جابجایی، جبر، BSE جبر سگال مجرد، نرم، BSE نرم عملگری
    Fatemeh Abtahi *, Maryam Toutounchi
    Let $(\mathcal A,\|\cdot\|_{\mathcal A})$ be a commutative and semisimple Banach algebra and $(\mathcal B,\|\cdot\|_{\mathcal B})$ be an abstract Segal algebra with respect to $\mathcal A$. In this paper, we first recall and study three important and practical mappings ${}_{\mathcal A}L$, $\Gamma_1$ and $\Gamma_2$. Then we investigatewhenever these mappings have closed ranges. In fact, we research and study the conditions, under which having closed range of one of these mappings implies having the closed range of the another mapping. After that, using these results, we give a necessary and sufficient condition for $(\mathcal B,\|\cdot\|_{\mathcal B})$, to be an algebra with $\rm BSE$ norm. Finally, we generalize some general results about abstract Segal algebras with respect to natural Banach functional algebras for abstract Segal algebras with respect to arbitrary Banach algebras. Also, throughout the paper, we provide examples to clarify the stated content.
    Keywords: Abstract Segal Algebra, BSE Algebra, BSE Function, BSE Norm, Commutative Banach Algebra
  • İlker ERYILMAZ

    Non-Newtonian Lebesgue spaces have emerged as a pivotal field in functional analysis, extending the classical Lebesgue spaces to encompass non-Newtonian Real numbers behaviors encountered in various physical and mathematical phenomena. This paper offers a comprehensive investigation into the properties, characteristics, and significance of Non-Newtonian Lebesgue spaces.


    Keywords: Non-Newtonian Numbers, Generator Function, ∗−Calculus, ∗− H¨Older’S Inequality, ∗−Minkowski Inequality, Nonnewtonian Lebesgue Space
  • Leila Musavizadeh Jazaeri, Leila Sharifan *
    This paper studies a repetitive polling game played on an n-vertex graph G. At first, each vertex is colored, Black or White. At each round, each vertex (simultaneously) recolors itself by the color of the majority of its closed neighborhood. The variants of the model differ in the choice of a particular tiebreaking rule. We assume the tie-breaking rule is Prefer-White and we study the relation between the notion of “dynamic monopoly” and “vertex cover” of G. In particular, we show that any vertex cover of G is a dynamic monopoly or reaches a 2−periodic coloring. Moreover, we compute dyn(G) for some special classes of graphs including paths, cycles and links of some graphs.
    Keywords: Repetitive Polling Game, Dynamic Monopoly, Vertex Cover, Majority Function
  • Maisoon Kulib, Ahmed Al-Gonah*

    This paper aims to introduce a new extension of extended Beta function by product of two Wright  functions. Various properties of this extended function are investigated such as integral representations, summation formulas and Mellin transform.‎

    Keywords: Extended Beta Function, Wright Function, Integral Representations, Summation Formula, Tricomi Function
  • Saeed Nazari Pasari, Naser Abbasi*, Ali Barani

    In this paper we establish new inequalities for convex and strongly convex defined on intervals in framework of Steffensen-Popoviciu and Dual Steffensen-Popoviciu measures are introduced. Some inequalities in this setting are also involved. Suitable examples are also involved are given.

    Keywords: Dual Steffensen-Popoviciu Measure, Convex Function, Strongly Convex Function, Coordinated Concave
  • Elham Mohammadi, Abbas Najati *, Iz-Iddine EL-Fassi
    Consider $Y$ as a real Hausdorff topological vector space and $(G,+)$ as a  Abelian group  uniquely divisible by 2. In this paper, the solutions and stability of the Pexiderized set-valued functional equations\begin{align*}    f(x+y)+f(x-y)+g(x+y)&=2f(x)+f(y)+f(-y)+g(x)\\    & \quad +g(y), \\    f(x+y)+f(x-y)+g(x+y)&=2f(x)+2f(y)+g(x)+g(y),\end{align*}are investigated, where $f$ and $g$ are unknown functions  from $G$ to $cc(Y)$.
    Keywords: Set-Valued Function, Quadratic Function, Drygas Function, Hukuhara Difference
  • Amirmasoud Kazemirad, Leila Golshani *, Vadood Najjari, Mohsen Kokabinezhad
    In this paper, hyperbolic and trigonometric functions, based on cosecant and cotangent as generator function for the family of Archimedean copula, are proposed. For these families, the dependence characteristics are compared. Also, to show the performance of these copulas, we investigate the stochastic frontier model based on them. Then we conclude that the copulas based on hyperbolic and trigonometric cosecant and cotangent are more suitable for modeling  dependence structure.
    Keywords: Archimedean Copula, Generator Function, Kendall's Tau, Spearman Rho, Stochastic Frontier Analysis
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