Journal of Mathematical Analysis and Convex Optimization
Volume:3 Issue: 1, 2022

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.

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.

‎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.

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.

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.

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.

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.

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.

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.

In this paper, the conditions are considered that a weighted Orlicz space, LΦw(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.