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Henstock-type integrals are studied for functions defined in a compact metric space T endowed with a regular σ-addltive measure μ, and taking values in a Banach lattice X. In particular, the space [0,1] with the usual Lebesgue measure is considered. The norm- and the order-type integral are compared and interesting results are obtained when X is an L-space. 2010 AMS Mathematics Subject Classification:...
The space-air-ground integrated network is based on the modern communication networks and integrated the latest communication and computer technologies, such that connects all various networks together to form a very huge and complicated network topology that has the best sharing of the global information and resources. This paper is treating the communication network as a space which is formed by...
Let C be a closed bounded convex subset of a Banach space X with 0 being an interior point of C and pC(.) be the Minkowski functional with respect to C. A generalized mutually maximization problem is said to be well posed if it has a unique solution (x, z) and every maximizing sequence converges strongly to (x, z). Under the assumption that the modulus of convexity with respect to pC(.) is strictly...
In this paper, I proved two strong convergence theorems of modified Ishikawa iteration and modified Halpern iteration for hemi-relatively nonexpansive mappings in a Banach space. The results presented in this work improve on the corresponding one announced by many others.
The purpose of this paper is to introduce and construct an iterative scheme by the viscosity approximation method for random nonexpansive mapping T in Banach spaces and to study that under suitable conditions this iterative process converges strongly to random fixed point of T .
We establish a strong convergence theorem for finding a common element of the set of fixed points of finite many relatively nonexpansive mappings and the set of solutions of an equilibrium problem in a Banach space by using a hybrid method. Our result extend and improve the recent one announced by Wataru Takahashi and Kei Zembayashi [Strong convergence theorem by a new hybrid method for equilibrium...
This paper presents a new implementable algorithm for solving the Lipschitz classifier that is a generalization of the maximum margin concept from Hilbert to Banach spaces. In contrast to the support vector machine approach, our algorithm is free to use any finite family of continuously differentiable functions which linearly compose the decision function. Nevertheless, robustness properties are maintained...
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