On the $$q$$ q -Derivatives of a Certain Linear Positive Operators

Some approximation properties of a new class of linear operators

“…The generalized Jain operators as variant of the Lupaş operators were studied by Patel and Mishra . Some related work in this area can be found in other works . Motivated by this, we give further modification of Jain operators in this paper with the help of a generalized Poisson‐type distribution, establish its convergence properties, and discuss its degree of approximation, asymptotic formula, and statistical convergence.…”

“…15 Some related work in this area can be found in other works. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Motivated by this, we give further modification of Jain operators in this paper with the help of a generalized Poisson-type distribution, establish its convergence properties, and discuss its degree of approximation, asymptotic formula, and statistical convergence. The results for the Szász-Mirakyan operators and Jain operators can be obtained from our operators as a particular case.…”

Some higher norm inequalities for composition of power operators

“…The norm estimate of operators applied to differential forms is an important and interesting research topic in some areas of mathematic analysis and has achieved fruitful results; see [1][2][3][4][5][6][7][8][9][10][11] for more detail. Some these results improved the development of some other branches of mathematics and mathematical physics; see [12][13][14][15][16][17][18] for details. In previous related research about norm estimates of operators the study mostly concentrated on estimates of the L t norm of operators and applying them to differential forms in terms of the L t norm of differential forms.…”

Simultaneous Approximation of New Sequence of Integral Type Operators with Parameter δ_0

“…Several new modifications of Szãsz sequence were constructed and studied, here we refer to [4,14,17,20]. Also,many authors have discussed the approximation behavior of different summation-integral type operators (see [6,7,10,12] )…”