Journal of Mathematical Extension
Volume:17 Issue: 9, Jan 2023

In this paper, we investigate the subclasses of harmonic univalent functions introduced by Porwal et al. in 2018. By implementing specific convolution operators such as the Pascal distribution series, we examine the inclusion relations of these functions. Moreover, we investigate several mapping properties involving these subclasses.

We define the Hausdorff MNC in the Hahn sequence space. Then, by applying the MNC we consider the solvability of BVP of frac- tional type by nonlocal integral boundary conditions in the Hahn se- quence space. Eventually, we provide one example to inquire the per- formance of main results.

Three ordinary differential equations are used to represent mathematically the breakdown of a phenol and pcresolcombination in a constantly agitated bioreactor.The research offers a stability analysis of the model’sequilibrium locations. Three different kernels have also been used to examine the effects of the fractaldimension and the fractional order on the model with the fractal-fractional derivatives. We have developedextremely effective computational techniques for phenol, p-cresol, and biomass concentrations. Finally,computer simulations are used to confirm the correctness of the suggested strategy.

Let G be a finite group and S be a subset of G such that 1G ̸∈ S and S −1 = S. The Cayley graph Σ = Cay(G, S) on G with respect to S is the graph with the vertex set G such that, for §, † ∈ G, the pair (§, †) is an arc in Cay(G, S) if and only if †§−1 ∈ S. The graph Σ is said to be arc-transitive if its full automorphism group Aut(Σ) is transitive on its arc set. In this paper we give a classification for arc-transitive Cayley graphs with valency six on finite abelian groups which are non-normal. Moreover, we classify all normal Cayley graphs on non-cyclic abelian groups with valency 6.

This paper aims at formulating definitions of topological stability‎, ‎structural stability‎, ‎and expansiveness property for an iterated functions system( abbrev‎, ‎IFS)‎. ‎It is going to show that the shadowing property is necessary condition for topological stability in IFSs‎. ‎Then‎, ‎it proves the previous weak converse demonstration with the addition of expansiveness property for IFSs‎. ‎Then‎, ‎by giving an example‎, ‎we show that in an IFS‎, ‎the shadowing property doesn't imply structural stability

The goal of this research is to construct the extended versions of the originalMaddox's paranormed sequence spaces, denoted by the notation $\ell(\nabla_q^2, p)$and $\ell_\infty(\nabla_q^2, p)$. These spaces are linear isomorphic to the spaces$\ell(p)$ and $\ell_\infty(p)$, respectively. The next step is to build the Schauder basisfor the $\ell(\nabla_q^2, p)$ space. After that, the topological features of the alpha, beta, and gammaduals of $\ell(\nabla_q^2, p)$ and $\ell_\infty(\nabla_q^2, p)$ are investigated. Finally, some matrix classes are characterized.