Journal of Calculus of Variations http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Some Approximation Properties of Modified Jain-Beta Operators Thu, 26 Dec 2013 11:16:32 +0000 http://www.hindawi.com/journals/jcv/2013/489249/ 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 , , and and discuss Voronovskaja asymptotic formula. Vishnu Narayan Mishra and Prashantkumar Patel Copyright © 2013 Vishnu Narayan Mishra and Prashantkumar Patel. All rights reserved. Some Approximation Properties of -Baskakov-Beta-Stancu Type Operators Mon, 16 Dec 2013 08:40:40 +0000 http://www.hindawi.com/journals/jcv/2013/814824/ This paper deals with new type -Baskakov-Beta-Stancu operators defined in the paper. First, we have used the properties of -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 -operators. Vishnu Narayan Mishra, Kejal Khatri, and Lakshmi Narayan Mishra Copyright © 2013 Vishnu Narayan Mishra et al. All rights reserved. Optimal Oil-Owner Behavior in Piecewise Deterministic Models Thu, 28 Nov 2013 16:06:39 +0000 http://www.hindawi.com/journals/jcv/2013/368096/ Six simple piecewise deterministic oil production models from economics are discussed by using solution tools that are available in the theory of piecewise deterministic optimal control problems. Atle Seierstad Copyright © 2013 Atle Seierstad. All rights reserved. Existence and Uniqueness of a Solution in the Space of BV Functions to the Equation of a Vibrating Membrane with a “Viscosity” Term Wed, 18 Sep 2013 09:40:01 +0000 http://www.hindawi.com/journals/jcv/2013/936915/ 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. Koji Kikuchi Copyright © 2013 Koji Kikuchi. All rights reserved. Algorithm for Solving a New System of Generalized Variational Inclusions in Hilbert Spaces Sun, 02 Jun 2013 09:44:59 +0000 http://www.hindawi.com/journals/jcv/2013/461371/ 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. Shamshad Husain and Sanjeev Gupta Copyright © 2013 Shamshad Husain and Sanjeev Gupta. All rights reserved.