Fixed Points of Involutions of G-Higgs Bundle Moduli Spaces over a Compact Riemann Surface with Classical Complex Structure Group

Antón-Sancho, Álvaro

doi:10.1007/s11464-023-0014-0

Front. Math

2024

DOI: 10.1007/s11464-023-0014-0

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Fixed Points of Involutions of G-Higgs Bundle Moduli Spaces over a Compact Riemann Surface with Classical Complex Structure Group

Álvaro Antón-Sancho

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Cited by 4 publications

References 14 publications

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Low-dimensional quadratic relative character varieties for the projective line minus three points

Simpson

2024

Sci. China Math.

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Low-dimensional quadratic relative character varieties for the projective line minus three points

Simpson

2024

Sci. China Math.

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Generalization of Fixed-Point Results in Complex-Valued Bipolar Metric Space with Applications

Shammaky,

Ahmad

2024

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We undertake this study with the objective of introducing certain control functions in the contractive condition to prove fixed-point theorems in the framework of complex-valued bipolar metric spaces. The incorporation of control functions broadens the applicability of the contractive condition. This approach yields key results consistent with previous studies. In support of our results, we offer two insightful examples that demonstrate the concepts discussed. Additionally, we present the notion of interpolative contraction in this new and generalized metric space and prove fixed-point theorems for non-self mappings. To demonstrate the application of our approach, we reproduce key findings from several established studies in the field.

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Exploring Fixed-Point Theorems in k-Fuzzy Metric Spaces: A Comprehensive Study

Nazam,

Attique,

Hussain

et al. 2024

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Recently, k -fuzzy metric spaces were introduced by connecting the degree of nearness of two points with k parameters (t1,t2,t3,⋯,tk) and the authors presented an analogue of Grabiec’s fixed-point result in k-fuzzy metric spaces along with other necessary notions. The results presented only addressed continuous mappings. For discontinuous mappings, there is no result in k-fuzzy metric spaces. In this paper, we obtain some fixed-point results stating necessary conditions for the existence of fixed points of mappings eliminating the continuity requirement in k-fuzzy metric spaces. We illustrate the hypothesis of our findings with examples. We provide a common fixed-point theorem and fixed-point theorems for single-valued k-fuzzy Kannan type contractions. As an application, we use a fixed-point result to ensure the existence of solution of fractional differential equations.

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Fixed Points of Involutions of G-Higgs Bundle Moduli Spaces over a Compact Riemann Surface with Classical Complex Structure Group

Cited by 4 publications

References 14 publications

Low-dimensional quadratic relative character varieties for the projective line minus three points

Low-dimensional quadratic relative character varieties for the projective line minus three points

Generalization of Fixed-Point Results in Complex-Valued Bipolar Metric Space with Applications

Exploring Fixed-Point Theorems in k-Fuzzy Metric Spaces: A Comprehensive Study

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