Journal of Mathematical Analysis and Convex Optimization
Volume:2 Issue: 2, 2021

In this paper, the chromatic polynomial structure on Riemannian manifolds and the almost golden structure on the tangent bundle of a Finsler manifold have been studied. A class of g-natural metrics on the tangent bundle of a Finsler manifold have been considered and some conditions under which the golden structure is compatible with the above-mentioned metric are proposed. The Levi-Civita connection associated with the mentioned metric is calculated and the results of it are presented. Finally, the integrability of the golden structure and its compatibility with the covariant derivative is studied.

‎The existence and number of limit cycles is an important problem ‎in the study of ordinary differential equations and dynamical‎ ‎systems‎. ‎In this work we consider $2$-dimensional predator-prey‎ ‎system and‎, ‎using Poincarchr('39'){e}-Bendixson theorem and LaSallechr('39')s‎ ‎invariance principle‎, ‎present some new necessary and some new‎ ‎sufficient conditions for the existence and nonexistence of limit‎ ‎cycles of the system‎. ‎These results extend and improve the‎ ‎previous results in this subject‎. ‎Local or global stability of the‎ ‎rest points of a system is also an important issue in the study of‎ ‎the equations and systems‎. ‎In this paper a sufficient condition‎ ‎about global stability of a critical point of the system will also‎ ‎be presented‎. ‎Our results are sharp and are applicable for‎ ‎predator-prey systems with functional response which is function‎ ‎of prey and predator‎. ‎At the end of the manuscript‎, ‎some examples‎ ‎of well-known predator-prey systems are provided to illustrate our‎ ‎results‎.

‎In this note‎, ‎we show that cite[Theorem 2.3]{ghorb} is not true‎. ‎In fact‎, ‎we show that $ell^{1}(mathbb{N}_{max})$ is a unital Banach algebra which is $phi$-pseudo amenable but it is not $phi$-approximate biflat for some $phiin Hom(ell^{1}(mathbb{N}_{max}))$‎.

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.

In economics, a production function relates the outputs of a production process to the inputs of the production. Generally, the production function is not available due to the complexity of the production process, the changes in production technology. Therefore, we have to consider an approximation of the production function. Data Envelopment Analysis (DEA) is a non-parametric methodology for obtaining an approximation of the production function and assessing the relative efficiency of economic units. Sensitivity analysis and sustainability evaluation of Decision Making Units (DMUs) are as the most important concerns of Decision Makers (DM). This study considers the sustainability radius of economic performance of DMUs and then proposes some approaches combined with sensitivity analysis for determining the sustainability radius of cost efficiency, revenue efficiency and profit efficiency of units. The proposed approaches eliminate the unit under evaluation from the observed data and disturb the data of it, based on the sensitivity analysis, to determine the sustainability radius of cost efficiency, revenue efficiency and profit efficiency of decision making units. Potential application of our proposed methods is illustrated with a dataset consisting of 21 medical centers in Taiwan.

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.

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 $mathbb{R}^2$.

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.

Common fixed point theorems for three self mappings satisfying generalized contractive conditions in cone metric spaces are derived. Also, some common fixed point results for two self mappings are deduced. Moreover, these all results generalize some important familiar results. Given example to illustrate our main result. Furthermore, an existence theorem for the common solution of the two Urysohn integral equations obtained by using our main result.

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.

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.

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.