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We give a precise example of a polynomial vector feld on $mathbb{R}^2$ whose corresponding singular holomorphic foliation of $mathbb{C}^2$ possesses a complex limit cycle which does not intersect the real plane $mathbb{R}^2$.

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In this paper, we introduce a new model of a block matrix operator  induced by two sequences and characterize its absolute-(p; r)-
∗-paranormality. Next, we give examples of these operators to show that absolute-(p; r)-∗-paranormal classes are distinct.
 

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In this article, we proposed a modified implicit iterative algorithm for approximation of common fixed point of finite families of two uniformly L-Lipschitzian total asymptotically pseudocontractive mappings in Banach spaces. Our new iterative algorithm contains some well known iterative algorithm which has been used by several authors for approximating fixed
points of different classes of mappings. We prove some convergence theorems of our new iterative method and validate our main result with a numerical ex-
ample. Our result is an improvement and generalization of the results of some well known authors in the existing literature.

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In this work, we will first propose an optimal three-step without-memory
method for solving nonlinear equations. Then, by introducing the self-accelerating
parameters, the with-memory-methods have been built. They have a fifty-nine
percentage improvement in the convergence order. The proposed methods have
not the problems of calculating the function derivative. We use these Steffensen-
type methods to solve nonlinear equations with simple zeroes with the appropri-
ate initial approximation of the root. we have solved a few nonlinear problems
to justify the theoretical study. Finally, are described the dynamics of the with-
memory method for complex polynomials of degree two.

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The main purpose of this article is to introduce and investigate the subcategory $mathcal{H}_{Sigma}(n,beta;phi)$ of bi-univalent functions in the open unit disk $mathbb{U}$ related to subordination. Moreover,  estimates on coefficient $|a_n|$ for functions belong to this subcategory are given applying different technique. In addition,  smaller upper bound and more accurate estimation than the previous outcomes are obtained.

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In this paper, we introduce a novel iterative scheme called quasi-implicit iterative scheme and study its stability as well as strong convergence for general class of maps in a normed linear space. Further, we proved rate of convergence and gave a numerical example to demonstrate that our iterative scheme is faster than semi- implicit iterative scheme and many more other iterative schemes in this direction.

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In the paper, we investigate Schur-convexity of differences which are obtained
from the Hermite-Hadamard type inequality for co-ordinated convex functions on a square
in plane. A generated Schur-convex sums by co-ordinated convex functions also is given.

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In this paper we introduce two new mapping in connection to Hermite-Hadamard type inequality. Some results concerning these mappings associated to the celebrated Hermite-Hadamard integral inequality for preinvex functions are given.
 

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In 1971 R. L. Carpenter proved that every derivation T on a semisimple commutative Frechet algebra A with identity is continuous. By relaxing the commutativity assumption on A and adding the surjectivity assumption on T, we derive a corresponding continuity result, for a new concept of almost derivations on Frechet algebras in this article. Also, it is further proved that every surjective almost derivation T on non commutative semisimple Frechet Q-algebras A with an additional condition on A, is continuous. Moreover, an example is provided to illustrate our main result.

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The construction of a nonnegative matrix for a given set of eigenvalues is one of the objectives of this paper. The generalization of the cases discussed in the previous papers as well as finding a recursive solution for the Suleimanova spectrum are other points that are studied in this paper.

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In this paper we consider the problem of characterizing linear maps on special $ star $-algebras behaving like left or right centralizers at orthogonal elements and obtain some results in this regard.

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‎Nonlinear problems in partial differential equations are open problems in many field of mathematics and engineering‎. ‎So associated with the structure of the problems‎, ‎many analytical and numerical methods are obtained‎. ‎We show that the differential transformation method is an appropriate method for the Dullin-Gottwald-Holm equation‎ (DGH), ‎which is a nonlinear partial differential equation arise in many physical phenomenon‎. ‎Hence in this paper‎, ‎the differential transform method (DTM) is applied to the Dullin-Gottwald-Holm equation‎. ‎We obtain the exact solutions of Dullin-Gottwald-Holm equation by using the DTM‎. ‎In addition‎, ‎we give some examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations‎. ‎These results show that this technique is easy to apply and provide a suitable method for solving differential equations‎. ‎To our best knowledge‎, ‎the theorem presented in Section 2 has been not introduced previously‎. ‎We presented and proved this new theorem which can be very effective for formulating the nonlinear forms of partial differential equations‎.

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Based on recent variational methods for smooth functionals defined on reflexive Banach spaces, We prove the existence of at least one
non-trivial solution for a class of  p-Hamiltonian systems. Employing one critical point theorem, existence of at least one weak solutions is ensured. This approach is based on variational methods and critical point theory. The technical approach is mainly based on the at least one non -trivial solution critical point theorem of G. Bonanno.

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In any Bayesian inference problem, the posterior distribution is a product of the
likelihood and the prior: thus, it is a ected by both in cases where one possesses little or no
information about the target parameters in advance. In the case of an objective Bayesian
analysis, the resulting posterior should be expected to be universally agreed upon by ev-
eryone, whereas . subjective Bayesianism would argue that probability corresponds to the
degree of personal belief. In this paper, we consider Bayesian estimation of two-parameter
exponential distribution using the Bayes approach needs a prior distribution for parame-
ters. However, it is dicult to use the joint prior distributions. Sometimes, by using linear
transformation of reliability function of two-parameter exponential distribution in order to
get simple linear regression model to estimation of parameters. Here, we propose to make
Bayesian inferences for the parameters using non-informative priors, namely the (depen-
dent and independent) Je reys' prior and the reference prior. The Bayesian estimation was
assessed using the Monte Carlo method. The criteria mean square error was determined
evaluate the possible impact of prior speci cation on estimation. Finally, an application on
a real dataset illustrated the developed procedures.

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We collection some results about maps on the algebra of all bounded operators that preserve the local spectrum and local spectral radius at nonzero vectors. Also, we described maps that preserve operators of local spectral radius zero at points and discuss several problems in this direction. Finally, we collection maps that preserve the local spectral subspace of operators associated with any singleton.
 

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The value of an auxiliary parameter incorporated into the well-known variational iteration method (VIM) to obtain solutions of wave equations in unbounded domains is discussed in this article. The suggested method, namely the optimal variational iteration method, is investigated for convergence. Furthermore, the proposed method is tested on one-dimensional and two-dimensional wave equations in unbounded domains in order to better understand the solution mechanism and choose the best auxiliary parameter.Comparisons with results from the standard variational iteration procedure demonstrate that the auxiliary parameter is very useful in tracking the convergence field of the approximate solution.

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The proximinality of certain subspaces of spaces of bounded affine functions is proved. The results presented here are some linear versions of an old result due to Mazur. For the proofs we use some sandwich theorems of Fenchel's duality theory.

 

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In this paper, the conditions are considered that a weighted Orlicz space, L^Φ_w(G), is a Banach algebra with convolution as  multiplication in context of a locally compact σ-compact groups. We also for a class of Orlicz spaces, obtain an equivalent condition, such that a weighted Orlicz space to be a convolution Banach algebra. This resultes generalized some known results in Lebesgue spaces.

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The aim of this paper is to investigate the existence and uniqueness of solution for a class of nonlinear integro-differential equations known as Hammerstein type. We study fractional equations in the Banach space whose derivative is of the Caputo type. The existence of solution is studied by using the Schauder's fixed point theorem, and the uniqueness is established via a generalization of the Banach fixed point theorem. Finally, an example is given to illustrate the analytical findings.

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A kind of approximation, called best coapproximation was

introduced and discussed in normed linear spaces by C. Franchetti and M.

Furi in 1972. Subsequently, this study was taken up by several researchers

in different abstract spaces.

In this paper, we define relations on best coapproximation and worst coapproximation. We show that

these relations are equivalence relation. We

obtain cosets sets of best coapproximation and worst approximation. We obtain some results on these

sets, compactness and weakly compactness and define coqproximinal and coqremotal.