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In the present paper, we study the mixed summation integral type operators having Baskakov and Szász basis functions in summation and integration form, respectively. We also give here the alternate form of the operators in terms of hypergeometric functions and estimated moments of these operators using hypergeometric series. In the last section, we present some results for operators related to convergence. [ABSTRACT FROM AUTHOR]

In this paper, a kind of modified Baskakov–Schurer–Szász operators (1.2) is introduced. Approximation properties of theses operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the convergence in certain weighted spaces is investigated. Furthermore, we study q -analogues of Baskakov–Schurer–Szász operators and its Stancu generalization. Then the better error estimations for the operators (6.3) by using King type approach is investigated. In the last section the Korovkin type weighted statistical approximation property of operators (9.1) is given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a simple integral generalization of q-analog of well known Bernstein operators with two parameters α and β, which was introduced in Mishra and Patel (2013) [17]. We give detail proof of the rate of convergence and Voronovskaja type asymptotic formula for the operators Dn, qα, β . Also, we establish statistical convergence for these operators and discuss modification of the operators Dn, qα, β for better approximation results over compact interval. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, a new theorem on the degree of approximation of function conjugate to a 2π periodic function f belonging to the generalized weighted Lipschitz -class by dropping the monotonicity condition on the generating sequence {pn } has been established which in turn generalizes the results of Lal (2009) [12] on Fourier series. We also note some errors appearing in the paper of Lal (2009) [12] and rectify them in the view of observations of Rhoades et al. (2011) [22]. [Copyright &y& Elsevier]

This paper implemented a stable numerical scheme for solving singularly perturbed linear second-order Fredholm integro-differential equation. A parameter-uniform numerical method was constructed using an exponentially fitted finite difference method to approximate the differential part and the composite Simpson 1/3 rule for the integral part of the equation. The scheme's stability and convergence analysis has been carried out. The maximum absolute errors and the rate of convergence are tabulated for different values of the perturbation parameter ɛ and mesh sizes using different numerical test examples. [ABSTRACT FROM AUTHOR]

• The concepts of mediative fuzzy relation as well as mediative fuzzy extension to handle the contradictory, non-contradictory and doubtful information have been developed. • The intuitionistic fuzzy projection and its extended concept i.e., mediative fuzzy projection has been defined. • The applicability of proposed mediative fuzzy projection in the medical field has been discussed in this work. • The impact and credibility of mediative factor in context of prediction work in relation to the proposed model has been shown in this work. The concept of fuzzy set, intuitionistic set, and mediative fuzzy set as a generalization of a crisp set have been introduced in many real-life applications. The concept of crisp relation between elements of sets can be extended to fuzzy relations. Extended relations will be considered as relations on fuzzy sets. In this work, we developed the concept of mediative fuzzy relation and meditative fuzzy projection in the context of fuzzy relation and fuzzy projection. We extended the basic operations of fuzzy projection into intuitionistic fuzzy projection and then in the mediative fuzzy projection. We have shown the credibility and impact of mediative index factor involves in the mediative fuzzy projection in context of prediction work in relation to the proposed model. Further, we applied the mediative fuzzy projection in the medical diagnosis in post-COVID-19 patients. The obtained results have also been discussed with their geometrical representation. [Display omitted] [ABSTRACT FROM AUTHOR]