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In this article, firstly we introduce weak statistical compactness and then, we prove a mean ergodic theorem by using this new concept. Since weak convergence implies weak statistical convergence, our result is a more generalization of Cohen,[3]. [ABSTRACT FROM AUTHOR]

In this article, we show that the existence theorem for fredholm type quadratic integral equation in the space of functions satisfying Hölder the condition, based on the classical Schauder fixed point theorem, has new methods that perform with relative compactness in the Hölder spaces. In section 3, some axioms are introduced to solve the fredholm integral equation. In section 4, one example is presented to verify the effectiveness and applicability of our results. [ABSTRACT FROM AUTHOR]

Snyder and Wilansky give the definition of semiconservative FK space and investigate the properties of this space in [5]. In their article, an FK space X containing ϕ is called semiconservative space if Xf ⊂ cs holds. In this paper, we study a new type of semiconservative space. Also, we give some characterizations of these spaces. [ABSTRACT FROM AUTHOR]