Common Fixed Point Theorems on Orthogonal Branciari Metric Spaces with an Application

In this article, we present the concept of orthogonal α-almost Istra˘tescu contraction of types D and D* and prove some fixed point theorems on orthogonal b-metric spaces. We also provide an illustrative example to support our theorems. As an application, we establish the existence and uniqueness of the solution of the fractional differential equation and the solution of the integral equation using Elzaki transform.

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New Fixed Point Results in Orthogonal B-Metric Spaces with Related Applications

Gnanaprakasam

Mani

Ege

et al. 2023

Mathematics

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On General Class of Z-Contractions with Applications to Spring Mass Problem

Alansari

Shagari

2023

Symmetry

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One of the latest techniques in metric fixed point theory is the interpolation approach. This notion has so far been examined using standard functional equations. A hybrid form of this concept is yet to be uncovered by observing the available literature. With this background information, and based on the symmetry and rectangular properties of generalized metric spaces, this paper introduces a novel and unified hybrid concept under the name interpolative Y-Hardy–Rogers–Suzuki-type Z-contraction and establishes sufficient conditions for the existence of fixed points for such contractions. As an application, one of the obtained results was employed to examine new criteria for the existence of a solution to a boundary valued problem arising in the oscillation of a spring. The ideas proposed herein advance some recently announced important results in the corresponding literature. A comparative example was constructed to justify the abstractions and pre-eminence of our obtained results.

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Fixed point theorem on an orthogonal extended interpolative $ \psi\mathcal{F} $-contraction

Dhanraj

Gnanaprakasam

Mani

et al. 2023

MATH

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<abstract><p>In this paper, we establish the fixed point results for an orthogonal extended interpolative Ciric Reich-Rus type $ \psi\mathcal{F} $-contraction mapping on an orthogonal complete $ \mathfrak{b} $-metric spaces and give an example to strengthen our main results. Furthermore, we present an application to fixed point results to find analytical solutions for functional equation.</p></abstract>

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Common Fixed Point Theorems on Orthogonal Branciari Metric Spaces with an Application

Cited by 3 publications

References 35 publications

New Fixed Point Results in Orthogonal B-Metric Spaces with Related Applications

New Fixed Point Results in Orthogonal B-Metric Spaces with Related Applications

On General Class of Z-Contractions with Applications to Spring Mass Problem

Fixed point theorem on an orthogonal extended interpolative $ \psi\mathcal{F} $-contraction

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