Some Approximation Properties of Modified Jain-Beta Operators

Generalization of Szász-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parameters α, β, and γ and discuss Voronovskaja asymptotic formula.

Some Approximation Properties of q-Baskakov-Beta-Stancu Type Operators

This paper deals with new type q-Baskakov-Beta-Stancu operators defined in the paper. First, we have used the properties of q-integral to establish the moments of these operators. We also obtain some approximation properties and asymptotic formulae for these operators. In the end we have also presented better error estimations for the q-operators.

Existence and Uniqueness of a Solution in the Space of BV Functions to the Equation of a Vibrating Membrane with a “Viscosity” Term

A nonlinear equation of motion of vibrating membrane with a “viscosity” term is investigated. Usually, the term is added, and it is well known that this equation is well posed in the space of functions. In this paper, the viscosity term is changed to , and it is proved that if initial data is slightly smooth (but belonging to is sufficient), then a weak solution exists uniquely in the space of BV functions.

Algorithm for Solving a New System of Generalized Variational Inclusions in Hilbert Spaces

We introduce and study a new system of generalized variational inclusions involving -cocoercive and relaxed -cocoercive operators, which contain the systems of variational inclusions and the systems of variational inequalities, variational inclusions, and variational inequalities as special cases. By using the resolvent technique for the -cocoercive operators, we prove the existence of solutions and the convergence of a new iterative algorithm for this system of variational inclusions in Hilbert spaces. An example is given to justify the main result. Our results can be viewed as a generalization of some known results in the literature.