In this paper, we present some fixed point results for generalized contraction in the framework of compete rectangular metric spaces. Further, we establish some fixed point theorems for this type of mappings defined on such spaces. Our results generalize and improve many of the well-known results. Moreover, to support our main results, we give an illustrative example.

/pdf/th-ph-contraction-on-a-e-complete-rectangular-b-metric-4c4v4482as.pdf

θ‐ϕ‐Contraction on α,η‐Complete Rectangular b‐Metric Spaces

The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions. In this paper, inspired by the concept of - contraction in metric spaces, introduced by Zheng et al., we present the notion of - contraction in - rectangular metric spaces and study the existence and uniqueness of a fixed point for the mappings in this space. Our results improve many existing results.

/pdf/new-fixed-point-theorems-for-th-ph-contraction-on-3yid8l90ah.pdf

New Fixed Point Theorems for θ ‐ ϕ -Contraction on Rectangular b -Metric Spaces

In the last few decades, a lot of generalizations of the Banach contraction principle had been introduced. In this paper, we present the notion of - contraction and - contraction in generalized asymmetric metric spaces to study the existence and uniqueness of the fixed point for them. We will also provide some illustrative examples. Our results improve many existing results.

/pdf/fixed-point-theorems-for-th-ph-contraction-in-generalized-4l24dkrut9.pdf

Fixed-Point Theorems for θ − ϕ -Contraction in Generalized Asymmetric Metric Spaces

In this paper, we define $\theta$-$\phi$-contraction on a $b$-metric space into itself by extending $\theta$-$\phi $-contraction introduced by Zheng {et al.} [D. W. Zheng, Z. Y. Cai, P. Wang, J. Nonlinear Sci. Appl., $\bf 10$ (2017), 2662--2670] in metric space and also, we prove $\theta $-type theorem in the setting of $b$-metric spaces as well as $\theta$-$\phi $-type theorem in the framework of $b$-rectangular metric spaces. Moreover, we give some applications to nonlinear integral equations. We also give illustrative examples to exhibit the utility of our results. 

New fixed point theorems for θ - ϕ -contraction on b -metric spaces

In this paper, we present the notion of expansive mapping in complete rectangular metric spaces and study various fixed point theorems for such mappings. The presented theorems extend, generalize, and improve many existing results in the literature.

/pdf/fixed-point-theorems-for-generalized-th-ph-expansive-mapping-3qodmy9tn2.pdf

Fixed Point Theorems for Generalized θ − ϕ − Expansive Mapping in Rectangular Metric Spaces

/pdf/new-fixed-point-theorems-for-theta-phi-contraction-in-1bh9y9xt89.pdf

New fixed point theorems for theta-phi contraction in complete metric spaces

As the real common generalisations of both orthodox transversals and adequate
 transversals in abundant semigroups, the concept of refined generalised
 quasi-adequate transversals, briefly, RGQA transversals was introduced by
 Kong and Wang. In this paper, for the RGQA transversal, the necessary and
 sufficient condition for the sets I and ? to be bands is investigated. It is
 demonstrated that the sets I and ? are both bands if and only if the RGQA
 transversal is weakly simplistic. Moreover, the RGQA transversal So being
 weakly simplistic is different from So being a quasi-ideal nor the abundant
 semigroup S satisfying the regularity condition. Finally, by means of a
 quasi-adequate semigroup and a band, the structure theorem for an abundant
 semigroup with a weakly simplistic RGQA transversal is established.

/pdf/abundant-semigroups-with-weakly-simplistic-rgqa-transversals-3r01u98o.pdf

Abundant semigroups with weakly simplistic RGQA transversals

In this paper, we study ﬁnite projective diﬀerential modules on p -adic polyannuli satisfying the Robba condition. Christol and Mebkhout proved the decomposition theorem (the p -adic Fuchs theorem) of such diﬀerential modules on one dimensional p -adic annuli under certain non-Liouvilleness assumption and Gachet generalized it to higher dimensional cases. On the other hand, Kedlaya proved a generalization of the p -adic Fuchs theorem in one dimensional case. We prove Kedlaya’s generalized version of p -adic Fuchs theorem in higher dimensional cases.

On generalized Fuchs theorem over $p$-adic polyannuli

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Papers

New fixed point theorems for theta-phi contraction in complete metric spaces

Abundant semigroups with weakly simplistic RGQA transversals

On generalized Fuchs theorem over $p$-adic polyannuli