Deferred Cesàro and deferred Euler equi-statistical convergence and its applications to Korovkin-type approximation theorem

Applications of statistical Riemann and Lebesgue integrability of sequence of functions

“…Recently, Mohiuddine and Alamri [8] studied Korovkin and Voronovskaya-type approximation theorems. For detailed study on Korovkin approximation theorem one may refer to [9,12,14,17]. By C[0, 1], we mean the space of all real valued continuous functions on [0,1].…”

Statistical Convergence via q-Calculus and a Korovkin’s Type Approximation Theorem

“…We prove a Korovkin type approximation theorem for q-statistical convergence analogous to that of given by Gadjiev and Orhan [30]. The Korovkin type approximation theorems have been proved by various authors through different summability methods; e.g., [38][39][40][41][42][43][44].…”

Fuzzy Korovkin type Theorems via deferred Cesaro and deferred Euler equi-statistical convergence

“…Demirci et al [14] proved a Korovkin type theorem by using equi-statistical convergence in the sense of power series method. Saini et al [31] presented the notions of equi-statistical convergence, pointwise statistical convergence and uniform statistical convergence for a sequence of real-valued functions by using deferred Cesáro and deferred Euler statistical convergence. Furthermore, the authors [31] established a Korovkin type theorem and the rate of convergence by using the notion of deferred Cesáro and deferred Euler equi-statistical convergence.…”

“…The purpose of the present paper is to extend the study carried out in [31] in the fuzzy environment. We establish the fuzzy Korovkin type approximation theorem for functions in C F (J b a ) by means of eq −stat D CE convergence and also determine the associated order of convergence via fuzzy modulus of continuity.…”