a characteriation of continuity of the $p$-$lambda$-variation function is given and the helly's selection principle for $lambda bv^{(p)}$ functions is established. a characterization of the inclusion of waterman-shiba classes into classes of functions with given integral modulus of continuity is given. a useful estimate on modulus of variation of functions of class $lambda bv^{(p)}$ is found.

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...

In the theory of mathematical optimization one try to find maximum or minimum points of functions depending of real variables and of other functions. Optimal control theory is a modern extension of the classical calculus of variations. Euler and Lagrange developed the theory of the calculus of variations in the eighteenth century. Its main ingredient is the Euler equation which was discovered a...

we prove that the limit of a sequence of pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable banach space is pettis integrable. then we provide basic properties for the pettis conditional expectation, and prove that it is continuous. calculus of pettis conditional expectations in general is very different from the c...

A discrete total variation calculus is presented in this paper. Using this calculus, we prove that the solution of the system of difference equations in Lee s discrete mechanics preserves a symplectic structure in the space–time sense. Numerical experiments are also reported. 2005 Elsevier Inc. All rights reserved.

McNamara and Dall (2011) identified novel relationships between the abundance of a species in different environments, the temporal properties of environmental change, and selection for or against dispersal. Here, the mathematics underlying these relationships in their two-environment model are investigated for arbitrary numbers of environments. The effect they described is quantified as the fit...