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In this paper we introduce and study two new properties (Bb) and (Bab) in connection with Weyl type theorems. It is shown that if T is a bounded linear operator acting on a Banach space X, then property (Bb) holds for T if and only if generalized Browder's theorem holds for T and π(T) = π 0 (T), where π(T) (resp., π 0 (T)) is the set of poles of resolvent of T (resp., the set of poles of resolvent of T of finite rank). A similar type of result has been obtained for property (Bab).

For modern wireless communication systems, miniaturized multiband antennas with enhanced bandwidth and gain are desired to achieve optimum system performance. A planar microstrip patch antenna is preferred because of its small size, low cost, and ease of fabrication. For impedance matching, a conductive metallic patch can be fed by different techniques to deliver the maximum power to the microstrip antenna. The various configurations of inset feed, co-axial feed, aperture feed, and proximity feed, and CPW feed, which are used to excite micro-strip patch antennas, are reviewed in this research paper. Different feeding mechanisms are discussed to improve antenna performance in terms of S11 parameter, bandwidth, gain, and radiation pattern suitable for different wireless communication applications.