English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We have constructed the sequence space    $(\Xi (\zeta ,t) )_{\upsilon }$  ( Ξ ( ζ , t ) ) υ , where    $\zeta =(\zeta _{l})$  ζ = ( ζ l ) is a strictly increasing sequence of positive reals tending to infinity and    $t=(t_{l})$  t = ( t l ) is a sequence of positive reals with    $1\leq t_{l}&lt;\infty $  1 ≤ t l &lt; ∞ , by the domain of    $(\zeta _{l})$  ( ζ l ) -Cesàro matrix in the Nakano sequence space    $\ell _{(t_{l})}$  ℓ ( t l ) equipped with the function    $\upsilon (f)=\sum^{\infty }_{l=0} ( \frac{ \vert \sum^{l}_{z=0}f_{z}\Delta \zeta _{z} \vert }{\zeta _{l}} )^{t_{l}}$  υ ( f ) = ∑ l = 0 ∞ ( | ∑ z = 0 l f z Δ ζ z | ζ l ) t l for all    $f=(f_{z})\in \Xi (\zeta ,t)$  f = ( f z ) ∈ Ξ ( ζ , t ) . Some geometric and topological properties of this sequence space, the multiplication mappings defined on it, and the eigenvalues distribution of operator ideal with  s -numbers belonging to this sequence space have been investigated. The existence of a fixed point of a Kannan pre-quasi norm contraction mapping on this sequence space and on its pre-quasi operator ideal formed by    $(\Xi (\zeta ,t) )_{\upsilon }$  ( Ξ ( ζ , t ) ) υ and  s -numbers is presented. Finally, we explain our results by some illustrative examples and applications to the existence of solutions of nonlinear difference equations.

journal of inequalities and applications

Solutions of nonlinear difference equations in the domain of $(\zeta _{n})$-Cesàro matrix in $\ell _{t(\cdot)}$ of nonabsolute type, and its pre-quasi ideal