Fixed point of ($$\psi ,\phi$$) contractions on metric spaces

Arya, M. C.; Chandra, Naresh; Joshi, Mahesh C.

doi:10.1007/s41478-019-00181-5

Cited by 3 publications

(3 citation statements)

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“…Thus, as of case I, we obtain that z is a common fixed point of T and S. In order to prove uniqueness, suppose that y is another common fixed point of T and S. Then Remark 2.9. Theorem 2.8 is a proper generalization of results due to Fei He et al [11] (Theorem 1.6) and the authors [2] (Theorem 1.7).…”

Section: Resultsmentioning

confidence: 56%

“…Next, we discuss an example which shows that Theorem 2.1 is more general than the results in [2,7,8,18,20].…”

Section: Resultsmentioning

confidence: 96%

“…Besides, many researchers have studied such types of contractive conditions and have been proved some interesting fixed point results for (ψ, φ)-contractive mappings, see [2,4,5,3,7,8,10,11,9,19,12,13,16,15,17,14,18,20] and references therein. Now, we establish two common fixed theorems for two mappings satisfying a generalized (ψ, φ)-rational contractive condition in a complete metric space.…”

Section: Theorem 14 ([7]mentioning

confidence: 99%

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Common fixed point results for a generalized ( ψ, φ )-rational contraction

Arya¹,

Chandra

Joshi

2023

Appl. Gen. Topol.

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Section: Resultsmentioning

confidence: 56%

“…Next, we discuss an example which shows that Theorem 2.1 is more general than the results in [2,7,8,18,20].…”

Section: Resultsmentioning

confidence: 96%

Section: Theorem 14 ([7]mentioning

confidence: 99%

See 1 more Smart Citation

Common fixed point results for a generalized ( ψ, φ )-rational contraction

Arya¹,

Chandra

Joshi

2023

Appl. Gen. Topol.

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Investigating fractal fractional PDEs, electric circuits, and integral inclusions via (ψ,ϕ)-rational type contractions

Aldwoah,

Shah,

Hussain

et al. 2024

Sci Rep

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The fixed point theory has been generalized mainly in two directions. One is the extension of the spaces, and the other is relaxing and generalizing the contractions. This paper aims to establish novel fixed point results of rational type generalized -contractions in the context of extended b-metric spaces. This will allow us to analyze generalized rational type contraction in a more relaxed and diversified framework in the light of the characteristics of . Some existing rational-type contractions have been recalled in this direction, and others are defined. New fixed point results have been established by utilizing the properties of and and applying the iteration technique. Moreover, the established results are employed to investigate the stability of fractal and fractional differential equations and electric circuits. For the reliability of the established results, examples and applications to the system of integral inclusions and system of integral equations are presented.

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