We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expecta...

The paper [3] started a new approach to Abstract Algebraic Logic in which, instead of the usual equivalence-based classification of logical systems leading to the well-known Leibniz hierarchy of protoalgebraic logics (see [5]), we proposed an alternative setting based on implication connectives. By studying the properties of weak p-implications (understood as generalized connectives defined by ...

In this work, we study the Neumann initial-boundary value problem for a two-species chemotaxis system with Lotka-Volterra competition and signal production. Under rather weak clean condition of sub-quadratic type damping merely integrable initial data, establish global existence generalized solutions in an N dimensional bounded smooth domain.

We define a regular m-partition of a distance regular graph as a partition of the vertex set into m classes, such that the number of vertices of a given class adjacent to a fixed vertex of another class (but possibly the same), is independent of the choice of that vertex in this class. Furthermore, we exhibit a technique to determine exact, discrete or bounding values for the intersection numbe...

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

Abstract: In this work, a nonsmooth multiobjective optimization problem involving generalized invexity with cone constraints and Applications (for short, (MOP)) is considered. The Kuhn-Tucker necessary and sufficient conditions for (MOP) are established by using a generalized alternative theorem of Craven and Yang. The relationship between weakly efficient solutions of (MOP) and vector valued s...

In this paper direct proofs of some common fixed point results for two and three mappings under weak contractive conditions are given. Some of these results are improved by using different arguments of control functions. Examples are presented showing that some generalizations cannot be obtained and also that our results are distinct from the existing ones.