Search

In this paper, we define a generalized resolvent operator involving a 풢 ⁢ (⋅ , ⋅) -co-monotone mapping for solving a generalized variational inclusion problem. We show that the resolvent operator under consideration is single-valued as well as Lipschitz continuous. An iterative algorithm is constructed to obtain the approximate solution of our problem. An example is provided to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper deals with the approximation properties of a generalized version of Szász–Mirakjan operators which preserve a x {a^{x}} , a > 1 {a>1} (fixed), and x ≥ 0 {x\geq 0}. The uniform convergence of the operators is studied by using some auxiliary results. Also, error estimations are determined by considering the functions from different spaces. The convergence of the said operators is shown and analyzed by graphics. In the same direction, the proposed operators are compared with Szász–Mirakjan operators for the rate of convergence. A Voronovskaya-type theorem is considered and a comparison with Szász–Mirakjan operators is shown in the sense of convexity. To describe the quantitative means of an asymptotic formula, we quantitatively approach the Voronovskaya-type theorem; moreover, a Grüss–Voronovskaya-type theorem is proved. For further investigations regarding the approximation for functions from various spaces, two significant extensions are added keeping in mind some developments in the L p {L_{p}} -space. One is the Kantorovich variant and the other one is the Durrmeyer modification of the defined operators. Here, the rate of convergence is described by means of the function with a derivative of bounded variation for the Durrmeyer modified operators for which some properties are discussed. Also, A-statistical properties of the Durrmeyer modified operators are established. This paper ends by presenting some significant statements and the conclusion. [ABSTRACT FROM AUTHOR]

In the present paper, we discuss the approximation properties of Jain–Baskakov operators with parameter c. The paper deals with the modified forms of the Baskakov basis functions. Some direct results are established, which include the asymptotic formula, error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct the King modification of these operators, which preserves the test functions e 0 {e_{0}} and e 1 {e_{1}}. It is shown that these King type operators provide a better approximation order than some Baskakov–Durrmeyer operators for continuous functions defined on some closed intervals. [ABSTRACT FROM AUTHOR]

Dynamics of composition of entire functions is well related to its factors, as it is known that for entire functions ƒ and g, ƒog has wandering domain if and only if goƒ has wandering domain. However the Fatou components may have different structures and properties. In this paper we have shown the existence of domains with all possibilities of wandering and periodic in given angular region θ. [ABSTRACT FROM AUTHOR]

Levels of fast escaping sets were discussed by Rippon and Stallard. Here we have defined a set BR(f) analogous to 0th level of fast escaping set by using maximum term and formation of spider's web structure has been discussed for this set. [ABSTRACT FROM AUTHOR]

In this paper we investigate a new (α , β) {(\alpha,\beta)} -metric F = β + a ⁢ α 2 + β 2 α {F=\beta+\frac{a\alpha^{2}+\beta^{2}}{\alpha}} , where α = a i ⁢ j ⁢ y i ⁢ y j {\alpha=\sqrt{{a_{ij}y^{i}y^{j}}}} is a Riemannian metric; β = b i ⁢ y i {\beta=b_{i}y^{i}} is a 1-form and a ∈ (1 4 , + ∞) {a\in(\frac{1}{4},+\infty)} is a real scalar. Also, we investigate the relationship between the geodesic coefficients of the metric F and the corresponding geodesic coefficients of the metric α. [ABSTRACT FROM AUTHOR]

In this paper, we first study a composite relaxed resolvent operator and prove some of its properties. After that, we introduce a Yosida approximation operator based on the composite relaxed resolvent operator and demonstrate some properties of the Yosida approximation operator. Finally, we obtain the solution of a system of Yosida inclusions by applying these concepts. We construct a conjoin example in support of many concepts derived in this paper. Our concepts and results are new in the literature and can be used for further research. [ABSTRACT FROM AUTHOR]

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators. [ABSTRACT FROM AUTHOR]

Approximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p , q) (p,q) -Baskakov operators, which reproduce the test function x 2 x^{2}. We have determined the order of approximation of the operators via K-functional and second order, the usual modulus of continuity, weighted and statistical approximation properties. In the end, some graphical results which depict the comparison with (p , q) (p,q) -Baskakov operators are explained and a Voronovskaja type result is obtained. [ABSTRACT FROM AUTHOR]