MSC: 47H05 47H09 47H10 47J25 65J15 Keywords: Strong convergence Equilibrium problem Quasi-φ-nonexpansive mapping Banach spaceThe purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of two quasi-φ-nonexpansive mappings and the set of solutions of an equilibrium problem in the framework of Banach spaces. Our results improve and extend the corresponding results announced by many others.

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.

Abstract:The discovery of new nanomaterials adds new dimensions to industry, electronics, and pharmaceutical and biological therapeutics. In this article, we first find closed forms of M-polynomials of polyhex nanotubes. We also compute closed forms of various degree-based topological indices of these tubes. These indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physico-chemical properties, such as boiling point, stability, and strain energy, of respective nanomaterial. To conclude, we plot surfaces associated to M-polynomials and characterize some facts about these tubes.

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