Premium
A certain class of weighted statistical convergence and associated Korovkin‐type approximation theorems involving trigonometric functions
Author(s) -
Srivastava H. M.,
Jena Bidu Bhusan,
Paikray Susanta Kumar,
Misra U. K.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4636
Subject(s) - mathematics , dominated convergence theorem , convergence (economics) , type (biology) , weak convergence , banach space , modes of convergence (annotated index) , class (philosophy) , normal convergence , compact convergence , discrete mathematics , rate of convergence , convergence tests , extension (predicate logic) , set (abstract data type) , pure mathematics , computer science , topological space , computer network , ecology , channel (broadcasting) , topological vector space , computer security , artificial intelligence , isolated point , economics , asset (computer security) , biology , economic growth , programming language
The subject of statistical convergence has attracted a remarkably large number of researchers due mainly to the fact that it is more general than the well‐established theory of the ordinary (classical) convergence. In the year 2013, Edely et al[17][Edely OHH, 2013] introduced and studied the notion of weighted statistical convergence. In our present investigation, we make use of the (presumably new) notion of the deferred weighted statistical convergence to present Korovkin‐type approximation theorems associated with the periodic functions 1 , cos x , and sin x defined on a Banach space C 2 π ( R ) . In particular, we apply our concept of the deferred weighted statistical convergence with a view to proving a Korovkin‐type approximation theorem for periodic functions and also to demonstrate that our result is a nontrivial extension of several known Korovkin‐type approximation theorems which were given in earlier works. Moreover, we establish another result for the rate of the deferred weighted statistical convergence for the same set of functions. Finally, we consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.