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In the present paper, a new theorem on the degree of approximation of a function [InlineEquation not available: see fulltext.], conjugate to a 2 π periodic function f belonging to the Lip α ([InlineEquation not available: see fulltext.]) class without the monotonicity condition on the generating sequence [InlineEquation not available: see fulltext.] has been established, which in turn generalizes the results of Lal (Appl. Math. Comput. 209: 346-350, 2009) on a Fourier series. MSC: 40G05, 41A10, 42B05, 42B08. [ABSTRACT FROM AUTHOR]

Recently, Lal (Appl. Math. Comput. 209:346-350, 2009) has determined the degree of approximation of a function belonging to Lip α and weighted [InlineEquation not available: see fulltext.]-classes using product [InlineEquation not available: see fulltext.] summability with non-increasing weights [InlineEquation not available: see fulltext.]. In this paper, we determine the degree of approximation of function [InlineEquation not available: see fulltext.], conjugate to a 2 π-periodic function f belonging to weighted [InlineEquation not available: see fulltext.]-class by dropping the monotonicity on the generating sequence [InlineEquation not available: see fulltext.] with a new (proper) set of conditions, which in turn generalizes the results of Mishra et al. (Bull. Math. Anal. Appl., 2013) on [InlineEquation not available: see fulltext.]-class and rectifies (removes) the errors of Mishra et al. (Mat. Vesn., 2013). Few examples and applications are also highlighted in this manuscript. MSC: Primary 42B05, 42B08, 40G05, 41A10. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new estimate for the degree of approximation of functions f (x , y) belonging to the generalized Lipschitz class L i p ((ξ 1 , ξ 2) ; r) , r ≥ 1 , by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from L i p ((α , β) ; r) and L i p (α , β) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and (C , γ , δ) means. [ABSTRACT FROM AUTHOR]

Runge's phenomenon reveals that interpolation methods lack uniform convergence of the sequence of the thus constructed polynomials to the function. The linear positive operators, however, can be relied on to ensure convergence across the whole domain. Further, linear positive operators can be modified suitably to approximate integrable functions. In this paper, we prove theoretical results on the estimates for the rate of approximation of a new sequence of operators. In addition, we find an error estimate for a larger class of functions, the functions of bounded variation. Finally, the theory is supported by suitable numerical examples, and the convergence estimates of the proposed operator are compared with the classical modified Bernstein–Durrmeyer operator. [ABSTRACT FROM AUTHOR]

In this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper "The within-host viral kinetics of SARS-CoV-2" published in (Math. Biosci. Eng. 17(4):2853–2861, 2020). Important properties of the model, like nonnegativity of solutions and their boundedness, are established. Also, we have calculated the basic reproduction number which is an important parameter in the infection models. From stability analysis of the model, it is found that stability of the biologically feasible steady states are determined by the basic reproduction number (χ 0) . Numerical simulations are done in order to substantiate analytical results. A biological implication from this study is that a COVID-19 patient with less than one basic reproduction ratio can automatically recover from the infection. [ABSTRACT FROM AUTHOR]

Inventory control is considered one of the most widely documented topics in the reality. Fractional derivatives and integration is the part of fractional calculus. Fractional calculus is the generalized part of ordinary calculus. The memory of physical phenomena is a highly concerning topic but it is neglected with describing in terms of integer-order differential equation. To discuss the memory of the inventory model, fractional derivative tools are considered. A fractional derivative at any point gives the previous marginal output and current point output for any current point input. In this model, a shortage is considered, and during the shortage period, demand is partially backlogged. Depending on the low partial backlogging rate and high partial backlogging rate, the result of the memory effect varies on the total average cost and optimal ordering interval. Moreover, in order to show the relationship between fractional models and ordinary classical model, two types of memory indices have been considered: (i) differential memory index and (ii) integral memory index. For a certain memory effect, minimized total average cost is the same for low partial backlogging rate and high partial backlogging rate. [ABSTRACT FROM AUTHOR]

We obtain global rates of approximation by qq-Durrmeyer operators Dn,q(f;x) for the functions in the class Lp([0,1]), 1 ≤ p ≤ ∞. First, rates of approximation in terms of the norms of f and f' and in terms of the ordinary modulus of smoothness are obtained. Subsequently, we obtain rates of approximation in terms of the generalized modulus of smoothness ωφ(f,δ). [ABSTRACT FROM AUTHOR]

In this paper, we define F-contractive type mappings in b-metric spaces and prove some fixed point results with suitable examples. F-expanding type mappings are also defined and a fixed point result is obtained. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce and study a sequence of positive linear operators defined on suitable spaces of measurable functions on [ 0 , ∞) and continuous function spaces with polynomial weights. These operators are Kantorovich type generalization of Jakimovski–Leviatan operators based on multiple Appell polynomials. Using these operators, we approximate suitable measurable functions by knowing their mean values on a sequence of subintervals of [ 0 , ∞) that do not constitute a subdivision of it. We also discuss the rate of convergence of these operators using moduli of smoothness. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of generalized nonexpansive mappings which is wider than the class of mappings satisfying (C) condition. Different properties and some fixed point results for these mappings are obtained here. The convergence of some iteration schemes to the fixed point is also discussed with suitable examples. [ABSTRACT FROM AUTHOR]