فهرست مطالب
Sahand Communications in Mathematical Analysis
Volume:20 Issue: 3, Summer 2023
- تاریخ انتشار: 1402/02/23
- تعداد عناوین: 10
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Pages 1-17In the 1920s, D. Hilbert has showed that the tensor of stress-energy, related to a given functional $\Lambda$, is a conservative symmetric bicovariant tensor $\Theta$ at the critical points of $\Lambda$, which means that div$\Theta =0$. As a routine extension, the bi-conservative condition (i.e. div$\Theta_2=0$) on the tensor of stress-bienergy $\Theta_2$ is introduced by G. Y. Jiang (in 1987). This subject has been followed by many mathematicians. In this paper, we study an extended version of bi-conservativity condition on the Lorentz hypersurfaces of the Einstein space. A Lorentz hypersurface $M_1^3$ isometrically immersed into the Einstein space is called $\mathcal{C}$-bi-conservative if it satisfies the condition $n_2(\nabla H_2)=\frac{9}{2} H_2\nabla H_2$, where $n_2$ is the second Newton transformation, $H_2$ is the 2nd mean curvature function on $M_1^3$ and $\nabla$ is the gradient tensor. We show that the $C$-bi-conservative Lorentz hypersurfaces of Einstein space have constant second mean curvature.Keywords: Lorentz hypersurface, bi-conservative, bi-harmonic, isoparametric
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Pages 19-31In this paper, we introduce a convolution-type product for strongly integrable Hilbert $C^*$-module valued maps on locally compact groups. We investigate various properties of this product related to uniform continuity, boundless, etc. For instance, we prove a convolution theorem. Also, we study the boundless of the related convolution operator in various settings.Keywords: Locally compact group, Convolution, Hilbert $C^*$-module, Fourier transform
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Pages 33-50In this paper, by employing sine hyperbolic inverse functions, we introduced the generalized subfamily $\mathcal{RK}_{\sinh}(\beta)$ of analytic functions defined on the open unit disk $\Delta:=\{\xi: \xi \in \mathbb{C} \text{ and } |\xi|<1 \}$ associated with the petal-shaped domain. The bounds of the first three Taylor-Maclaurin's coefficients, Fekete-Szeg\"{o} functional and the second Hankel determinants are investigated for $f\in\mathcal{RK}_{\sinh}(\beta)$. We considered Borel distribution as an application to our main results. Consequently, a number of corollaries have been made based on our results, generalizing previous studies in this direction.Keywords: Analytic function, Bounded turning function, convex function, Subordination, Fekete-Szego functional, Hankel determinant, Borel distribution
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Pages 51-68Let $\varphi:A\to B$ be an isomorphism of $C^*$-algebras and $I$ be an ideal of $A.$ Introducing the concepts of unitary equivalent and the implemented Finsler modules, we show that the $\frac{A}{I}$-module $\frac{E}{E_{I}}$ and the implemented $\frac{B}{\varphi(I)}$-module $\frac{F}{F_{\varphi(I)}}$ are unitary equivalent. We also, establish a one to one correspondence between the groups $U(E)$ and $U(F)$ of unitaries on full Finsler modules $E$ and $F,$ respectively. Finally, we explain regularized dynamical systems and apply the aforementioned one to one correspondence to prove that each regularized dynamical system in $U(E)$ implements a regularized dynamical system in $U(F).$Keywords: $C^*$-Dynamical systems, generalized derivation, Finsler module, ternary derivation, one parameter group, unitary operator
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Pages 69-80In this work, we consider product-type operators $T^m_{u,v,\varphi}$ from minimal M\"{o}bius invariant spaces into Zygmund-type spaces. Firstly, some characterizations for the boundedness of these operators are given. Then some estimates of the essential norms of these operators are obtained. Therefore, some compactness conditions will be given.Keywords: Essential norm, Generalized Stevic-Sharma type operators, Zygmund type spaces, Minimal Mobius invariant spaces
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Pages 81-96In this paper, we introduce the class of strongly $m$--$MT$-convex functions based on the identity given in [P. Cerone et al., 1999]. We establish new inequalities of the Ostrowski-type for functions whose $n^{th}$ derivatives are strongly $m$--$MT$-convex functions.Keywords: Integral inequality, MT-convex functions, Strongly MT-convexity, Strongly m-MT-convexity
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Pages 97-108In the literature, several papers are devoted to inequalities of Simpson-type in the case of differentiable convex functions and fractional versions. Moreover, some papers are focused on inequalities of Simpson-type for twice differentiable convex functions. In this research article, we obtain an identity for twice differentiable convex functions. Then, we prove several fractional inequalities of Simpson-type for convex functions.Keywords: Simpson type inequalities, Twice differentiable convex functions, Riemann-Liouville fractional integrals, Fractional calculus
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Pages 109-132This article deals with the existence, uniqueness and Ulam type stability results for a class of boundary value problems for fractional differential equations with Riesz-Caputo fractional derivative. The results are based on Banach contraction principle and Krasnoselskii's fixed point theorem. An illustrative example is given to validate our main results.Keywords: Riesz-Caputo fractional derivative, existence, Measure of noncompactness, Fixed point, Ulam stability, Non-instantaneous impulses
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Pages 133-156A system of generalized mixed variational inclusion problem (SGMVIP) is considered involving $H(.,.)$-mixed mappings in $q$-uniformly smooth Banach spaces. By means of proximal-point mapping method, the existence of solution of this system of variational inclusions is given. A new two-step iterative algorithm is proposed for solving SGMVIP. Strong convergence of the proposed algorithm is given.Keywords: System of generalized mixed variational inclusion problem, H(., .)-mixed mappings, Proximal-point mapping
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Pages 157-177In this paper, we define and consider, the category {\bf FPos}-$S$ of all $S$-fuzzy posets and action-preserving monotone maps between them. $S$-fuzzy poset congruences which play an important role in studying thecategorical properties of $S$-fuzzy posets are introduced. More precisely, the correspondence between the $S$-fuzzy poset congruences and the fuzzy action and order preserving maps is discussed. We characterize $S$-fuzzy poset congruences on the $S$-fuzzy posets in terms of the fuzzy pseudo orders. Some categorical properties of the category {\bf FPos}-$S$ of all $S$-fuzzy posets is considered. In particular, we characterize products, coproducts, equalizers, coequalizers, pullbacks and pushouts in this category. Also, we consider all forgetful functors between the category {\bf FPos}-$S$ and the categories {\bf FPos} of fuzzy posets, {\bf Pos}-$S$ of $S$-posets, {\bf Pos} of posets, {\bf Act}-$S$ of $S$-acts and {\bf Set} of sets and study the existence of their left and right adjoints. Finally, epimorphisms, monomorphisms and order embeddings in {\bf FPos} and {\bf FPos}-$S$ are studied.Keywords: Fuzzy poset, $S$-fuzzy congruence, Free object, Cofree object, Adjoint pair