Statistically and Relatively Modular Deferred-Weighted Summability and Korovkin-Type Approximation Theorems

Symmetry

HariMohan Srivastava¹  Umakanta Misra²  BiduBhusan Jena³  SusantaKumar Paikray³ 

[1] Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada;Department of Mathematics, National Institute of Science and Technology, Palur Hills, Golanthara, Odisha 761008, India;Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha 768018, India;

关键词: statistical convergence;    P-convergent;    statistically and relatively modular deferred-weighted summability;    relatively modular deferred-weighted statistical convergence;    Korovkin-type approximation theorem;    modular space;    convex space;    N-quasi convex modular;    N-quasi semi-convex modular;   

DOI  :  10.3390/sym11040448

来源: DOAJ

【 摘 要 】

The concept of statistically deferred-weighted summability was recently studied by Srivastava et al. (Math. Methods Appl. Sci. 41 (2018), 671–683). The present work is concerned with the deferred-weighted summability mean in various aspects defined over a modular space associated with a generalized double sequence of functions. In fact, herein we introduce the idea of relatively modular deferred-weighted statistical convergence and statistically as well as relatively modular deferred-weighted summability for a double sequence of functions. With these concepts and notions in view, we establish a theorem presenting a connection between them. Moreover, based upon our methods, we prove an approximation theorem of the Korovkin type for a double sequence of functions on a modular space and demonstrate that our theorem effectively extends and improves most (if not all) of the previously existing results. Finally, an illustrative example is provided here by the generalized bivariate Bernstein–Kantorovich operators of double sequences of functions in order to demonstrate that our established theorem is stronger than its traditional and statistical versions.

【 授权许可】

Unknown