On Quasi b-Metric Space with index k and fixed point results

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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Extraction new results of common fixed point theorems for $({T}, {\alpha }_{{s}}, {F})$-contraction of six mappings in a tripled b-metric space with an application of integral equations

Journal of Inequalities and Applications ◽

10.1186/s13660-020-02503-9 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Ghorban Khalilzadeh Ranjbar ◽

Mohammad Esmael Samei

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Integral Equations ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Common Solution ◽

Type Integral ◽

First Time ◽

Common Fixed Point Theorems

Abstract The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$ α s -admissible, triangular partially triple weakly $\alpha _{s}$ α s -admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, we present a new model, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.

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Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽

10.3390/sym13030501 ◽

2021 ◽

Vol 13 (3) ◽

pp. 501

Author(s):

Ahmed Boudaoui ◽

Khadidja Mebarki ◽

Wasfi Shatanawi ◽

Kamaleldin Abodayeh

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fixed Points ◽

Metric Space ◽

Fixed Point Theorems ◽

Coupled Fixed Point ◽

Sufficient Conditions ◽

Impulsive Differential Equations ◽

System Of Differential Equations ◽

Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

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Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space

Symmetry ◽

10.3390/sym13010032 ◽

2020 ◽

Vol 13 (1) ◽

pp. 32

Author(s):

Pragati Gautam ◽

Luis Manuel Sánchez Ruiz ◽

Swapnil Verma

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Real Number ◽

Metric Space ◽

Contraction Mapping ◽

Metric Spaces ◽

Rectangular Metric Space ◽

New Type ◽

Symmetry Requirement ◽

Definition Of

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

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