In this paper, we tighten the concise Turán theorem for irregular graphs, using spectral and non-spectral proofs. We then investigate to what extent Turán’s theorem can be similarly strengthened for generalized r-partite graphs.

A spectral mapping theorem is proved that resolves a key problem in applying invariant manifold theorems to nonlinear Schrodinger type equations. The theorem is applied to the operator that arises as the linearization of the equation around a standing wave solution. We cast the problem in the context of space-dependent nonlinearities that arise in optical waveguide problems. The result is, howe...

This paper proposes a prototypical environment for gamut mapping in spectral space. Images are rendered in terms of light and material parameters by a symbolic ray tracer, and the parameter ranges are adjusted, without re-rendering, to bring the image into the output device’s spectral gamut. There is a growing disparity between the high dynamic range images produced by spectral renderers and th...

for an evolution family (U(t, s))t≤s≤0 on X . We refer to [5, 12] where these equations have been introduced and to [10, 13] for concrete examples. In particular, we showed in [12] that (1.1) and the abstract Cauchy problem associated to an operator ( ,D( )) on the product space := X × L(R−,X) are “equivalent.” Since, under appropriate conditions, the operator ( ,D( )) is the generator of a str...

A classic result in extremal graph theory, known as Mantel's theorem, states that every non-bipartite of order n with size m>⌊n24⌋ contains a triangle. Lin, Ning and Wu [Comb. Probab. Comput. 30 (2021) 258-270] proved spectral version theorem for given n. Zhai Shu [Discrete Math. 345 (2022) 112630] investigated fixed m. In this paper, we prove Q-spectral versions theorem.

In the present paper, we establish a fixed point theorem for a mapping and a common fixed point theorem for a pair of mappings. The mapping involved here generalizes various type of contractive mappings in integral setting.

The Fixed Point Theorem had been proved on Reciprocally Continuous Self Mapping. In this paper the fixed point theorem on reciprocally continuous self mapping is proved under Menger Space.