Generalized convexity and optimization problems
Generalized differential equations in the space of regulated functions (boundary value problems and controllability)
Boundary value problems for generalized linear differential equations and the corresponding controllability problems are dealt with. The adjoint problems are introduced in such a way that the usual duality theorems are valid. As a special case the interface boundary value problems are included. In contrast to the earlier papers by the author the right-hand side of the generalized differential equations as well as the solutions of this equation can be in general regulated functions (not necessarily...
Generalized directional derivatives for locally Lipschitz functions which satisfy Leibniz rule
Generalized distributivity for real, continuous functions. II: Local solutions in the continuous case.
Generalized domains of semistable attraction of nonnormal laws.
Generalized Fractional Calculus With Application in Mechanics
Generalized Fractional Evolution Equation
2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does not admit a probabilistic...
Generalized fractional integrals on central Morrey spaces and generalized λ-CMO spaces
We introduce the generalized fractional integrals and prove the strong and weak boundedness of on the central Morrey spaces . In order to show the boundedness, the generalized λ-central mean oscillation spaces and the generalized weak λ-central mean oscillation spaces play an important role.
Generalized gradient flow and singularities of the Riemannian distance function
Significant information about the topology of a bounded domain of a Riemannian manifold is encoded into the properties of the distance, , from the boundary of . We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of , as well as applications to homotopy equivalence.
Generalized function fractional integration operators in some classes of analytic functions
Generalized Hardy operators and normalizing measures.
Generalized Hardy's inequality
Generalized inequalities for indefinite forms.
Generalized invexities and global minimum properties.
Generalized iterated function systems, multifunctions and Cantor sets
Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.
Generalized Lazarevic's inequality and its applications. II.
Generalized matrix versions of the Cauch-Schwarz and Kantorovich inequalities.
Generalized midconvexity
There are many types of midconvexities, for example Jensen convexity, t-convexity, (s,t)-convexity. We provide a uniform framework for all the above mentioned midconvexities by considering a generalized middle-point map on an abstract space X. We show that we can define and study the basic convexity properties in this setting.
Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields
Generalized multivariate Jensen-type inequality.