In this article, we explore the concept of the prequasi norm on Nakano special space of sequences (sss) such that its variable exponent in 0 , 1 . We evaluate the sufficient setting on it with the definite prequasi norm to configuration prequasi Banach and closed (sss). The Fatou property of different prequasi norms on this (sss) has been investigated. Moreover, the existence of a fixed point of Kannan prequasi norm contraction maps on the prequasi Banach (sss) and the prequasi Banach operator ideal constructed by this (sss) and s − numbers have been examined.

In this manuscript, a new family of contractions called Jaggi-type hybrid G − ϕ -contraction is introduced and some fixed point results in generalized metric space that are not deducible from their akin in metric space are obtained. The preeminence of this class of contractions is that its contractive inequality can be extended in a variety of manners, depending on the given parameters. Consequently, several corollaries that reduce our result to other well-known results in the literature are highlighted and analyzed. Substantial examples are constructed to validate the assumptions of our obtained theorems and to show their distinction from corresponding results. Additionally, one of our obtained corollaries is applied to set up unprecedented existence conditions for the solution of a family of integral equations.

In this article, we investigate the notion of the pre-quasi norm on a generalized Cesàro backward difference sequence space of non-absolute type $(\Xi (\Delta,r) )_{\psi }$ ( Ξ ( Δ , r ) ) ψ under definite function ψ. We introduce the sufficient set-up on it to form a pre-quasi Banach and a closed special space of sequences (sss), the actuality of a fixed point of a Kannan pre-quasi norm contraction mapping on $(\Xi (\Delta,r) )_{\psi }$ ( Ξ ( Δ , r ) ) ψ , it supports the property (R) and has the pre-quasi normal structure property. The existence of a fixed point of the Kannan pre-quasi norm nonexpansive mapping on $(\Xi (\Delta,r) )_{\psi }$ ( Ξ ( Δ , r ) ) ψ and the Kannan pre-quasi norm contraction mapping in the pre-quasi Banach operator ideal constructed by $(\Xi (\Delta,r) )_{\psi }$ ( Ξ ( Δ , r ) ) ψ and s-numbers has been determined. Finally, we support our results by some applications to the existence of solutions of summable equations and illustrative examples.

In this article, we investigate the sufficient conditions on weighted Nakano sequence space to be premodular Banach (sss). We examine some topological and geometrical structures of the multiplication operators defined on weighted Nakano prequasi-normed (sss).