On the functional equation $${\varvec{f}}({\varvec{x}})+{\varvec{f}}({\varvec{y}})=\mathbf{max} \{{\varvec{f}}({\varvec{xy}}),{\varvec{f}}({\varvec{xy}}^{-{\varvec{1}}})\}$$f(x)+f(y)=max{f(xy),f(xy-1)} on groups
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DOI: 10.1007/s00013-017-1061-0
Abstract: We analyse the functional equation $$\begin{aligned} f(x)+f(y)=\max \{f(xy),f(xy^{-1})\} \end{aligned}$$f(x)+f(y)=max{f(xy),f(xy-1)}for a function $$f:G\rightarrow \mathbb R$$f:G→R where G is a group. Without further assumption it characterises the absolute value of additive functions. In addition $$\{z\in G\mid f(z)=0\}$${z∈G∣f(z)=0}… read more here.
Keywords: varvec varvec; varvec; functional equation; max ... See more keywords
Rational Type Multivalued $$\varvec{F}_{\varvec{G}}$$FG-Contractive Mappings with a Graph
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DOI: 10.1007/s00025-018-0813-x
Abstract: In the present study we aim to present new fixed point results for multivalued maps on a metric space. To do this, we define a new type contraction, that is, rational type multivalued $$F_{G}$$FG-contraction, on… read more here.
Keywords: varvec varvec; varvec contractive; type multivalued; rational type ... See more keywords
On Stability of the Thomson’s Vortex N-gon in the Geostrophic Model of the Point Vortices in Two-layer Fluid
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DOI: 10.1007/s00332-018-9526-2
Abstract: A two-layer quasigeostrophic model is considered. The stability analysis of the stationary rotation of a system of N identical point vortices lying uniformly on a circle of radius R in one of the layers is… read more here.
Keywords: varvec varvec; case; stability; beta ... See more keywords
$$(\varvec{k},\varvec{a})$$(k,a)-generalized wavelet transform and applications
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DOI: 10.1007/s11868-019-00291-5
Abstract: We introduce the notion of the (k, a)-generalized wavelet transform. Particular cases of such generalized wavelet transform are the classical and the Dunkl wavelet transforms. The restriction of the (k, a)-generalized wavelet transform to radial functions is… read more here.
Keywords: wavelet; varvec varvec; applications varvec; wavelet transform ... See more keywords