We do not live by hype, or skin, alone, it appears; what we live by, in these jumpy times, is the last shreds of the saving hope that someone is thinking through the hype, that the body bared is the end product of an analytic sequence or a good workout program.
Thus, (y mn ) is a p- metric of the double analytic sequence and an p- metric of double analytic sequence.
Thus, (y mn ) is a p- metric of double analytic sequence and, hence, an p- metric of double analytic sequence.
Thus, (y mn ) is a p- metric paranormed space of double analytic sequence and, hence, an p- metric double analytic sequence.
For any sequence of Musielak functions f = (f mn ) and q = (q mn ) be double analytic sequence of strictly positive real numbers.
This implies that it yields lim uv μ mn (x) = 0, and hence, x = (x mn ) ∈ w2 is λ− convergent to 0. Let f = (f mn ) be a Musielak-modulus function, (X,∥(d x1),d(x2),⋯,d(xn−1))∥ p ) be a p-metric space, and q = (q mn ) be double analytic sequence of strictly positive real numbers.
Let f = ( f mn ) be a Musielak-modulus function and q = (q mn ) be a double analytic sequence of strictly positive real numbers; the sequence spaces χ f μ 2 q, d x 1, d x 2, ⋯, d x n − 1 p φ Open image in new windowand Λ f μ 2 q, d x 1, d x 2, ⋯, d x n − 1 p φ Open image in new windoware linear spaces.
Let f = ( f mn ) be a Musielak-modulus function and q = (q mn ) be a double analytic sequence of strictly positive real numbers; the sequence space χ f μ 2 q, d x 1, d x 2, ⋯, d x n − 1 p φ Open image in new windowis a paranormed space with respect to the paranorm defined by g ( x ) = inf f mn μ mn ( x ), d x 1, d x 2, ⋯, d x n − 1 p φ q mn 1 / H ≤ 1, Open image in new window.
For any Musielak-modulus function f = (f mn ) and a double analytic sequence q = (q mn ) of strictly positive real numbers, the space χ f μ 2 qA, d x 1, d x 2, ⋯, d x n − 1 p φ Open image in new windowis a topological linear space paranormed by g ( x ) = inf f mn A mn μ mn ( x ), d x 1, d x 2, ⋯, d x n − 1 p φ q mn 1 / H ≤ 1, Open image in new window.
The vector space of all double analytic sequences will be denoted by Λ2.
