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In this study, we introduce the class of generalized Stolz mappings by generalized approximation numbers . Also we prove that the class of ℓ α p −type mappings are included in the class of generalized Stolz mappings by generalized approximation numbers and we define a new quasinorm equivalent with T α φ (p) . Further we give a new class of operator ideals by using generalized approximation numbers and symmetric norming function and we show that this class is an operator ideal.

In this study, by using the Catalan conservative matrix, we define a new paranormed sequence space ℓfalse(trueC˜,pfalse) and show that the space ℓfalse(trueC˜,pfalse) is linearly isomorphic to ℓ(p). Also, we determine dual spaces and the Schauder basis of the resulting space.

In this paper, we define a new class of s-type (, ; ()) operators, , ,. Also we show that this class is a quasi-Banach operator ideal and we study on the properties of the classes which are produced via different types of s-numbers.

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