A coincident point principle for two weakly compatible mappings in partial S-metric spaces

In this research, we establish some new fixed-point results for a symmetric coupled dominated fuzzy mapping satisfying a new advanced contraction on a closed ball in the setting of complete fuzzy metric spaces. In addition, the new notion of hybrid fuzzy-graph-dominated mappings introduced in fuzzy metric spaces achieves some new advanced fuzzy fixed-point problems. Some new definitions and illustrative examples are given to validate our new findings. Lastly, to demonstrate the originality of our new results, we present an application to the Fredholm-type integral equation.

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Fixed point approach to solve fractional differential equations in $ S^{JS} $-metric spaces

Rizk

Souayah

Mlaiki

2022

MATH

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<abstract>This study aims to establish a new fixed point theorem in the framework of $ S^{JS} $-metric spaces, recently introduced by Beg et al. We propose different principles of contraction using various techniques. The theorems obtained represent a new framework for other future work in the considered space. Also, we provide two applications of our results to linear system of equations and the following fractional differential equation <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \mathcal{(P)}:\left\{ \begin{array}{ccl} D^{\lambda}x(t) & = & f(t, x(t)) = Fx(t) \mbox{ if } t\in I_0 = (0, T] \\ x(0) & = & x(T) = r \ \end{array} \right\}. $\end{document} </tex-math></disp-formula> These applications show the effectiveness of our approach as a powerful tool for solving several types of differential equations.</abstract>

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A coincident point principle for two weakly compatible mappings in partial S-metric spaces

Abstract: We show the existence of common fixed point and a coincident point for two weakly compatible selfmappings defined on a complete partial S-metric space X, where the contraction in the assumption of the main result has three control functions, α, ψ, φ.

Cited by 5 publications

References 13 publications

Some Valid Generalizations of Boyd and Wong Inequality andψ,ϕ-Weak Contraction in Partially Orderedb−Metric Spaces

Some Valid Generalizations of Boyd and Wong Inequality andψ,ϕ-Weak Contraction in Partially Orderedb−Metric Spaces

Symmetrical Hybrid Coupled Fuzzy Fixed-Point Results on Closed Ball in Fuzzy Metric Space with Applications

Fixed point approach to solve fractional differential equations in $ S^{JS} $-metric spaces

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