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ISSN : 1226-0657
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Vol.11 No.3
Abstract
The purpose of the present paper is to study the generalized CR-sub manifold of a T-manifold. After preliminaries we have studied the integrability of the distributions and obtained the conditions for integrability. Then geometry of leaves are being studied. Finally it is proved that every totally umbilical generalized CR-submanifold of a T-manifold is totally geodesic.
Abstract
In this article, using the L'Hospital rule, mathematical induction, the trigonometric power formulae and integration by parts, some integral formulae for the improper integrals <TEX>${\int}_0^{\infty}$</TEX>[sin<TEX>$^{2m}({\alpha}x)]/(x^{2n})dx$</TEX> AND <TEX>${\int}_0^{\infty}$</TEX>[sin<TEX>$^{2m+1}({\alpha}x)]/(x^{2n+1})dx$</TEX> are established, where m <TEX>$\geq$</TEX> n are all positive integers and <TEX>$\alpha$</TEX><TEX>$\neq$</TEX> 0.
Abstract
Let W(z) be a power series with operator coefficients such that multiplication by W(z) is contractive in extC(z). The overlapping space <TEX>$\varepsilon$</TEX>(W) of D(W) in C(z) is a Herglotz space with Herglotz function <TEX>$\varphi$</TEX>(z) which satisfies <TEX>$\varphi$</TEX>(z) + <TEX>${\varphi}^*(z^{-1})$</TEX> = 2[1-W<TEX>$^*(z^{-1})W(z)]$</TEX>.
Abstract
In this paper, we introduce the concepts of interior of a fuzzy set and several types of fuzzy compactness and fuzzy RS-compactness in a redefined fuzzy topological space and investigate their properties.
Abstract
In this paper, we introduce weakly relaxed <TEX>$\alpha$</TEX>-pseudomonotonicity and weakly relaxed <TEX>$\alpha$</TEX>-semi-pseudomonotonicity of set-valued maps. Using the KKM technique, we obtain existence of solutions to the variational-like inequalities with weakly relaxed <TEX>$\alpha$</TEX>-pseudomor.otone set-valued maps in reflexive Banach spaces. We also present the solvability of the variational-like inequalities with weakly relaxed <TEX>$\alpha$</TEX>-semi-pseudomonotone set-valued maps in arbitrary Banach spaces using Kakutani-Fan-Glicksberg fixed point theorem.
Abstract
In this paper, we introduce the fundamental concepts of intuitionistic fuzzy Q-neighborhood, intuitionistic Q-first axiom of countability, intuitionistic first axiom of countability, intuitionistic fuzzy closure operator, intuitionistic fuzzy boundary point and intuitionistic fuzzy accumulation point and investigate some of their properties.