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Abstract: Abstract In this article, we obtain the strong convergence of the new modified Halpern iteration process $$\begin{aligned} x_{n+1} = \alpha _{n}u + (1-\alpha _{n})T_{n}P(x_{n} + \theta _{n}(x_{n} - x_{n-1})), \ \ \ \ \ \ n=1,2,3,\ldots , \end{aligned}$$ to a common fixed point of \(\{ T_{n}\}\) , where \(\{ T_{n}\}_{n=1}^{\infty }\) is a family of nonexpansive mappings on the closed and convex subset C of a Banach space X, \(P: X \longrightarrow C\) is a nonexpansive retraction, \(\{\alpha _n\} \subset [0, 1]\) and \(\{\theta _n\}\subset R^+\) . Some applications of this result are also presented. PubDate: 2022-05-12

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Abstract: Abstract In this paper, we establish a sequential formula for the subdifferential of multi-composed convex functions via an interesting result due to (Bot et al. in J Math Anal Appl 342(2):1015–1025, 2008), based on perturbation theory. As an application, we derive sequential optimality conditions for a convex fractional programming problem with geometric and cone constraints, without considering any qualification condition. We give an example illustrates the general result where no exact subdifferential optimality conditions are possible without a regularity condition such that sequential subdifferential conditions are more meaningful. PubDate: 2022-05-05

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Abstract: Abstract Let R be a semiprime ring with center Z(R) and \(\lambda \) a nonzero left ideal of R. A mapping \(F: R\rightarrow R\) (not necessarily additive) is said to be a multiplicative (generalized)-derivation on R, if there exists a map d (not necessarily an additive map or derivation) on R such that \(F(xy)=F(x)y+xd(y)\) holds for all \(x,y\in R\) . Suppose that F and G are two multiplicative (generalized)-derivations of R associated with the maps d and g respectively on R. Throughout this paper we study the following situations: \(F([x,y])+G(yx)+d(x)F(y)+xy \in Z(R)\) , \(F(x\circ y)+G(yx)+d(x)F(y)+xy \in Z(R)\) , \(F(xy)+G(yx)+d(x)F(y)\pm [x, y] \in Z(R)\) , \(F([x,y])+G(xy)+d(x)F(y)+yx \in Z(R)\) , \(F(x\circ y)+G(xy)+d(x)F(y)+yx \in Z(R)\) , \(F([x,y])+G(yx)+d(y)F(x)-xy \in Z(R)\) , \(F(x)F(y)-G(yx)-xy+yx \in Z(R)\) ; for all \(x,y\in \lambda \) . PubDate: 2022-05-03

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Abstract: Abstract In this article, we obtain the strong convergence of the new modified Halpern iteration process $$\begin{aligned} x_{n+1} = \alpha _{n}u + (1-\alpha _{n})T_{n}P(x_{n} + \theta _{n}(x_{n} - x_{n-1})), \ \ \ \ \ \ n=1,2,3,\ldots , \end{aligned}$$ to a common fixed point of \( \{ T_{n} \}\) , where \(\{ T_{n}\}_{n=1}^{\infty }\) is a family of nonexpansive mappings on the closed and convex subset C of a Banach space X, \(P: X \longrightarrow C\) is a nonexpansive retraction, \(\{\alpha _n\} \subset [0, 1]\) and \(\{\theta _n\}\subset R^+\) . Some applications of this result are also presented. PubDate: 2022-05-03

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Abstract: Abstract We study the composition operators on certain weighted Hilbert spaces \({\mathcal {H}} _\omega\) , consisting of analytic functions defined on \({\mathbb {D}}\) , that can be described as a weighted Dirichlet space with weight \(\omega\) having certain properties. We will use the notion of vanishing \(\omega\) -Carleson measure to characterize the compact composition operators on \({\mathcal {H}} _\omega\) . Also, we give some upper and lower estimates for the essential norm of these operators and investigate the Hilbert-Schmidt composition operators. PubDate: 2022-04-30

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Abstract: Abstract In this paper, we are concerned with the study of a critical (p, q) equation with Hardy terms on the Heisenberg group. Existence of entire solutions is obtained via an application of some concentration–compactness type results and the mountain pass theorem. Our results are presented in the model case of the (p, q) horizontal Laplacian equations, but the method can be extended to deal with a more general class of problems with operators of (p, q) growth. PubDate: 2022-04-28

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Abstract: Abstract In this work, we prove weak convergence of a single-step iterative algorithm to a solution of variational inequality problems in 2-uniformly convex and uniformly smooth real Banach spaces. We apply our main result to the Nash-Cournot equilibrium oligopoly electricity market. We also give some numerical examples in infinite dimensional setting to illustrate how our algorithm works. Finally, our results generalize and complement several existing results in the literature. PubDate: 2022-04-28

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Abstract: Abstract In this paper generalized Kantorovich operators are constructed using Lototsky-Bernstein basis functions on unit interval. An approximation of continuous functions by these sequence of operators has been established based on Korovkin’s theorem. Finally, we prove that this sequence of operators \(D_{\mu }(f;x)\) converges to \(f\in L^{p}[0,1]\) in \(\Vert .\Vert _{p}\) . PubDate: 2022-04-26

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Abstract: Abstract In this paper, we study instability of solitary wave solutions of the generalized two space-dimensional Benjamin equation \((u_t+u_{xxx}-\beta {\mathscr {H}}u_{xx}+(u^p)_x)_x=u_{yy}\) . This equation governs the evolution of waves at the interface of a two-fluid system in which surface-tension effects cannot be ignored. We improve the previous work by Chen et al. (Proc R Soc A 464:49–64, 2008, https://doi.org/10.1098/rspa.2007.0013) to the case \(\beta <0\) and \(p>7/3\) , and show that solitary waves of this equation are unstable by the mechanism of blow-up. PubDate: 2022-04-22

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Abstract: Abstract Combining the ideas of Ishikawa iteration and mean iteration, we establish weak convergence theorems for finding common fixed points of nonlinear mappings. The mappings are not necessarily continuous or commutative. We consider a class of mappings which includes nonexpansive mappings, generalized hybrid mappings and normally 2-generalized hybrid mappings as special cases. Our result generates many alternative iteration schemes to approximate common fixed points of nonlinear mappings and improves many existing theorems in the literature. PubDate: 2022-04-19

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Abstract: Abstract Let \(\lambda _{sym^{2}f}(n)\) be the \(n^{th}\) normalized Fourier coefficient of symmetric square L-function. In this paper, we will establish an asymptotic formula for $$\begin{aligned} \sum _{{\mathop {(a,b,c,d)\in \mathbb {Z}^{4}}\limits ^{a^{2}+b^{2}+c^{2}+d^{2}\le {x}}}}\lambda ^{\theta }_{sym^{2}f}(a^{2}+b^{2}+c^{2}+d^{2}) \end{aligned}$$ where \(\theta =3,4\) and \(x\ge {x_{0}}\) (sufficiently large). PubDate: 2022-04-12

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Abstract: Abstract The aim of the paper is to study the commuting generalized derivations. Suppose that R is a prime ring of char \((R)\ne 2\) , \(\pi (\xi _1,\ldots ,\xi _n)\) is a noncentral multilinear polynomial over C and \(T_1\) , \(T_2\) and \(T_3\) are generalized derivations on R. If \(T_2(\xi )T_1(\xi )=T_1(\xi )\xi -\xi T_3(\xi )\) for all \(\xi =\pi (\xi _1,\ldots ,\xi _n)\in f(R)\) , then we describe all possible forms of \(T_1\) , \(T_2\) and \(T_3\) . PubDate: 2022-04-07

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Abstract: Abstract It is well known that an hyponormal operator satisfies Weyl’s theorem. A result due to Conway shows that the essential spectrum of a normal operator N consists precisely of all points in its spectrum except the isolated eigenvalues of finite multiplicity, that’s \(\sigma _{e}(N)=\sigma (N)\setminus E^0(N).\) In this paper, we define and study a new class named \((W_{e})\) of operators satisfying \(\sigma _{e}(T)=\sigma (T)\setminus E^0(T),\) as a subclass of (W). A counterexample shows generally that an hyponormal does not belong to the class \((W_{e}),\) and we give an additional hypothesis under which an hyponormal belongs to the class \((W_{e}).\) We also give the generalization class \((gW_{e})\) in the context of B-Fredholm theory, and we characterize \((B_{e}),\) as a subclass of (B), in terms of localized SVEP. PubDate: 2022-04-04

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Abstract: Abstract Let \((C(t))_{t\in \mathbb {R}}\) be a strongly continuous cosine operators on a Banach space X into itself and let A be their infinitesimal generator. In this work, we study the uniform convergence of the Abel averages \(\lambda \int _{0}^{\infty }e^{-\lambda t}C(t)dt\) of C(t) when \(\lambda \) tends to \(0^+\) . More precisely, we show that C(t) is uniformly Abel ergodic if and only if \( {X}= {\mathcal {R}}(A)\oplus {\mathcal {N}}(A)\) , with \( {\mathcal {R}}(A)\) and \( {\mathcal {N}}(A)\) the range and the kernel of A, respectively. Next, we examine this theory with the uniform power convergence of the Abel average \(\lambda ^2 R(\lambda ^2, A)\) , for some \(\lambda >0\) , where \(R(\lambda ^2,A)\) be the resolvent function of A. PubDate: 2022-04-01

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Abstract: Abstract The purpose of this paper is to introduce an algorithm for approximating solutions of split equality variational inequality problems. A convergence theorem of the proposed algorithm is established in Hilbert spaces under the assumption that the associated mapping is uniformly continuous, pseudomonotone and sequentially weakly continuous. Finally, we provide several applications of our method and provide a numerical result to demonstrate the behavior of the convergence of the algorithm. Our results extend and generalize some related results in the literature. PubDate: 2022-04-01

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Abstract: Abstract Let U be the Utumi quotient ring of a prime ring R, char \((R)\ne 2\) and \(f(x_1,\ldots ,x_n)\) be a noncentral multilinear polynomial over the extended centroid C. Suppose that G, F and H are three generalized derivations on R such that \(F(G(f(r))f(r))-H(f(r)^2)=0\) for all \(r=(r_1,\ldots ,r_n)\in R^{n}\) . In this paper, we give the complete characterization of the mappings G, F and H. PubDate: 2022-04-01

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Abstract: Abstract In this paper, we study the existence of multiple solutions for the boundary value problem $$\begin{aligned} \begin{array}{llll} -\Delta _{\gamma } u&{}= f(x,u) + g(x,u) &{} \text{ in } &{} \Omega , \\ u&{}= 0 &{} \text{ on } &{} \partial \Omega , \end{array} \end{aligned}$$ where \(\Omega\) is a bounded domain with smooth boundary in \(\mathbb {R}^N \ (N \ge 2),\) \(f(x,\xi ), g(x,\xi )\) are Carathéodory functions, \(f(x,\xi )\) is odd in \(\xi\) , \(g(x,\xi )\) is perturbation term and \(\Delta _{\gamma }\) is the strongly degenerate elliptic operator of the type $$\begin{aligned} \Delta _\gamma : =\sum \limits _{j=1}^{N}\partial _{x_j} \left( \gamma _j^2 \partial _{x_j} \right) , \quad \partial _{x_j}: =\frac{\partial }{\partial x_{j}},\quad \gamma : = (\gamma _1, \gamma _2,\ldots , \gamma _N). \end{aligned}$$ We use the minimax method and Rabinowitz’s perturbation method. This result is a generalization of that of Luyen and Tri (Complex Var Elliptic Equ 64(6):1050–1066, 2019). PubDate: 2022-04-01

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Abstract: Abstract In this paper one of the possible p-operator space structures of the p-analog of the Fourier-Stieltjes algebra will be introduced, and to some extend will be studied. This special sort of p-operator structure will be given from the predual of this Fourier type algebra, that is the algebra of universal p-pseudofunctions. Furthermore, some applicable and expected results will be proven. Current paper can be considered as a new gate into the collection of problems around the p-analog of the Fourier-Stieltjes algebra, in the p-operator space structure point of view. PubDate: 2022-04-01

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Abstract: Abstract This paper deals with some existence results based on Schauder’s and Monch’s fixed point theorems and the technique of the measure of noncompactness for Cauchy problem of Caputo–Fabrizio fractional differential equations with not instantaneous impulses. Some illustrative examples are presented in the last section. PubDate: 2022-04-01

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Abstract: Abstract Some problems in the theory of approximation of functions on the sphere \(\sigma ^{m-1}\) in the metric of \(S^{(p,q)}\) by functions with bounded spectrum, are investigated. We prove analogues of Jackson’s direct theorem for the moduli of smoothness of all orders constructed on the basis of spherical shift. The equivalence between moduli of smoothness and K-functional for the couple \(\left( S^{(p,q)}(\sigma ^{m-1}), W^{r}_{p,q}(\sigma ^{m-1})\right) \) is also shown on the sphere \(\sigma ^{m-1}\) . PubDate: 2022-04-01