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Some approximation results involving the q ‐Szász–Mirakjan–Kantorovich type operators via Dunkl's generalization
Author(s) -
Srivastava H. M.,
Mursaleen M.,
Alotaibi Abdullah M.,
Nasiruzzaman Md.,
AlAbied A. A. H.
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.4397
Subject(s) - mathematics , modulus of continuity , generalization , bivariate analysis , lipschitz continuity , type (biology) , exponential function , rate of convergence , pure mathematics , exponential type , order (exchange) , mathematical analysis , statistics , ecology , channel (broadcasting) , finance , electrical engineering , economics , biology , engineering
The purpose of this paper is to introduce a family of q ‐Szász–Mirakjan–Kantorovich type positive linear operators that are generated by Dunkl's generalization of the exponential function. We present approximation properties with the help of well‐known Korovkin's theorem and determine the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K ‐functional, and the second‐order modulus of continuity. Furthermore, we obtain the approximation results for bivariate q ‐Szász–Mirakjan–Kantorovich type operators that are also generated by the aforementioned Dunkl generalization of the exponential function. Copyright © 2017 John Wiley & Sons, Ltd.