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Abstract In this paper we present a new method of determining Koebe domains. We apply this method by giving a new proof of the well-known theorem of A. W. Goodman concerning the Koebe domain for the class T of typically real functions. We applied also the method to determine Koebe sets for...
Abstract Modelling of singularities given by discontinuous functions or Schwartz distributions by means of generalized functions of Colombeau has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions that model singularities given by...
Abstract In this paper, we introduce a new class of general mixed vector F -implicit complementarity problems and general mixed vector F -implicit variational inequality problems, and study the equivalence between of them under certain assumptions in Banach spaces. We also derive some new...
Abstract Under a class of generalized (Type I, F , ρ )-convexity assumptions, the author formulates the sufficient conditions about Pareto efficiency and Geoffrion proper efficiency and gets the dual results between multiobjective programming and its Wolfe dual.
Abstract Sufficient optimality criteria are derived for a control problem under generalized invexity. A Mond-Weir type dual to the control problem is proposed and various duality theorems are validated under generalized invexity assumptions on functionals appearing in the problems. It is pointed...
Abstract We study a particular class of transition kernels that stems from differentiating Markov kernels in the weak sense. Sufficient conditions are established for this type of kernels to admit a Jordan-type decomposition. The decomposition is explicitly constructed.
We establish fairly general sufficient conditions for a locally compact group (a Baire topological group) to admit partitions into finitely many congruent μ -thick (everywhere of second category) subsets.
Abstract It is known that a Fréchet space 𝔽 can be realized as a projective limit of a sequence of Banach spaces . The space K c (𝔽) of all compact, convex subsets of a Fréchet space, 𝔽, is realized as a projective limit of the semilinear metric spaces . Using the notion of Hukuhara...
Abstract A nonlinear multiobjective programming problem is considered. Weak, strong and strict converse duality theorems are established under generalized second order ( F, α, ρ, d )-convexity for second order Mangasarian type and general Mond-Weir type vector duals.
Abstract This paper concerns the existence and multiplicity of positive solutions for a class of nonresonant m -point boundary-value problem of second-order differential equations Lx = λw ( t )ƒ( t , x ), 0 < t < 1. The interesting points are that Lx ≔ – x ″ + ρqx and w is L p...
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