The Cesáro Lacunary Ideal bounded linear operator of χ2 - of φ-statistical vector valued defined by a bounded linear operator of interval numbers

Abstract

Let   uv mn A be a sequence of bounded linear operators from a separable Banach metric space of (X , 0) into a Banach metric space (Y, 0). Suppose that φ ∈ Φ is a countable fundamental set of X and the ideal I - of subsets \mathbb{N} x \mathbb{N} has property (AP). The sequence   uv mn A is said to be * b I - convergent if it is pointwise I - convergent and there exists an index set K such that \mathbb{N} x \mathbb{N} / K I and   , uv mn m n K A x  is bounded for any x ∈ X , the concept of lacunary vector valued of χ2 and the concept of Δ11 - lacunary statistical convergent vector valued of χ2 of difference sequences have been introduced. In addition, we introduce interval numbers of asymptotically ideal equivalent sequences of vector valued difference by Musielak fuzzy real numbers and established some relations related to this concept. Finally we introduce the notion of interval numbers of Cesáro Orlicz asymptotically equivalent sequences vector valued difference of Musielak Orlicz function and establish their relationship with other classes.

Keywords

• Banach metric
• bounded linear operator
• ideal
• Iconvergence
• analytic sequence
• Museialk-Orlicz function
• double sequences
• chi sequence
• Lambda
• Riesz space
• strongly
• statistical convergent
• lacunary refinement