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
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
Abstract We have constructed the sequence space $(\Xi (\zeta ,t) )_{\upsilon }$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>Ξ</mml:mi><mml:mo>(</mml:mo><mml:mi>ζ</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow><mml:mi>υ</mml:mi></mml:msub></mml:math> , where $\zeta =(\zeta _{l})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ζ</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>ζ</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:math> is a strictly increasing sequence of positive reals tending to infinity and $t=(t_{l})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:math> is a sequence of positive reals with $1\leq t_{l}<\infty $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo><</mml:mo><mml:mi>∞</mml:mi></mml:math> , by …