On (<em>m</em>, <em>w</em>)-Generalized Group Inverse in a Banach Algebra
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By combining the sum of a weighted group inverse and a quasinilpotent element, we introduce an extension of the m-weak and generalized group inverses in a Banach *-algebra. We develop various properties and representations of this weighted generalized inverse. Furthermore, we apply this new generalized inverse to complex matrices and solve a minimization problem.