On the Monotonicity of Positive Linear Operators

On Some Refinements of Jensen's Inequality

“…We have come to know that the monotonicity of Bernstein Stancu operators was also proved by Horova and Budikova [14] recently; however, they used direct calculations. M. K. Khan et al [17] provide some converse results concerning the monotonicity of operators of probability type. Now we mix inequality (6) with more information about the function f to obtain sharper results about the sequence of approximation operators.…”

A Korovkin type approximation theorems via $$\mathcal{I}$$ -convergence

“…where U is an arbitrary interval of ¡ , the set of all real numbers, and g is a nonnegative increasing function on [0, ∞) with g(0) = 1, and also C(U ) denotes the linear space of all real-valued continuous functions on U (see, for instance, [12]; also [6]). …”

On the preservation of log convexity and log concavity under some classical Bernstein-type operators

“…with {N t : t 0} being a standard Poisson process, that is, with independent and stationary increments such that for every t > 0, N t follows a Poisson distribution with mean equal to t. • The Baskakov operator [2,7,8,10,12,13] …”