• Title/Summary/Keyword: rational contraction mappings

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SOME FIXED POINT RESULTS ON DOUBLE CONTROLLED CONE METRIC SPACES

  • A. Herminau Jothy;P. S. Srinivasan;Laxmi Rathour;R. Theivaraman;S. Thenmozhi
    • Korean Journal of Mathematics
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    • v.32 no.2
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    • pp.329-348
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    • 2024
  • In this text, we investigate some fixed point results in double-controlled cone metric spaces using several contraction mappings such as the B-contraction, the Hardy-Rogers contraction, and so on. Additionally, we prove the same fixed point results by using rational type contraction mappings, which were discussed by the authors Dass. B. K and Gupta. S. Also, a few examples are included to illustrate the results. Finally, we discuss some applications that support our main results in the field of applied mathematics.

NEW APPROXIMATE FIXED POINT RESULTS FOR VARIOUS CYCLIC CONTRACTION OPERATORS ON E-METRIC SPACES

  • R. THEIVARAMAN;P. S. SRINIVASAN;S. RADENOVIC;CHOONKIL PARK
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.27 no.3
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    • pp.160-179
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    • 2023
  • In this paper, we investigate the existence and diameter of the approximate fixed point results on E-metric spaces (not necessarily complete) by using various cyclic contraction mappings, including the B-cyclic contraction, the Bianchini cyclic contraction, the Hardy-Rogers cyclic contraction, and so on. Additionally, we prove the approximate fixed point results for rational type cyclic contraction mappings, which were discussed mainly in [35] and [37], in the setting of E-metric space. Also, a few examples are provided to demonstrate our findings. Subsequently, we discuss some applications of approximate fixed point results in the field of applied mathematics rigorously.

SOME FIXED POINT RESULTS FOR TAC-SUZUKI CONTRACTIVE MAPPINGS

  • Mebawondu, Akindele A.;Mewomo, Oluwatosin T.
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1201-1222
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    • 2019
  • In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type F-contraction and modified TAC-(${\psi}$, ${\phi}$)-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al. [9], Rhoades [18], Doric, [8], Khan et al. [13], Wardowski [25], Piri et al. [17], Sing et al. [23] and many more results in this direction.

COMMON FIXED POINT THEOREMS UNDER RATIONAL CONTRACTIONS IN COMPLEX VALUED EXTENDED b-METRIC SPACES

  • Vairaperumal, V.;Raj, J. Carmel Pushpa;Joseph, J. Maria;Marudai, M.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.4
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    • pp.685-700
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    • 2021
  • In this paper, we discuss the existence and uniqueness of fixed point and common fixed point theorems in complex valued extended b-metric spaces for a pair of mappings satisfying some rational contraction conditions which generalized and unify some well-known results in the literature.

F-CONTRACTION IN PARTIALLY ORDERED b-METRIC LIKE SPACES

  • Om Prakash Chauhan;Vishal Joshi;Saurabh Singh
    • The Pure and Applied Mathematics
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    • v.31 no.1
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    • pp.103-117
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    • 2024
  • In this article, we utilize the concepts of hybrid rational Geraghty type generalized F-contraction and to prove some fixed point results for such mappings are in the perspective of partially ordered b-metric like space. Some innovative examples are also presented which substantiate the validity of obtained results. The example is also authenticated with the help of graphical representations.

FIXED POINT THEOREM OF 𝜓s-RATIONAL TYPE CONTRACTIONS ALONG WITH ALTERING DISTANCE FUNCTIONS IN b-METRIC SPACES

  • Oratai Yamaod;Atit Wiriyapongsanon
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.3
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    • pp.769-779
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    • 2024
  • In this paper, we introduce the new concept of 𝜓s-rational type contractive mapping in the sense of 𝑏-metric spaces. Also, we obtain some fixed point results for these contractive mappings in complete b-metric spaces. Our main results generalize, extend and improve the corresponding results on the topics given in the literature. Finally, we also give some examples to illustrate our main results.

SOME FIXED POINT THEOREMS FOR RATIONAL (𝛼, 𝛽, Z)-CONTRACTION MAPPINGS UNDER SIMULATION FUNCTIONS AND CYCLIC (𝛼, 𝛽)-ADMISSIBILITY

  • Snehlata, Mishra;Anil Kumar, Dubey;Urmila, Mishra;Ho Geun, Hyun
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.4
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    • pp.757-771
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    • 2022
  • In this paper, we present some fixed point theorems for rational type contractive conditions in the setting of a complete metric space via a cyclic (𝛼, 𝛽)-admissible mapping imbedded in simulation function. Our results extend and generalize some previous works from the existing literature. We also give some examples to illustrate the obtained results.

Existence of Solutions of Integral and Fractional Differential Equations Using α-type Rational F-contractions in Metric-like Spaces

  • Nashine, Hemant Kumar;Kadelburg, Zoran;Agarwal, Ravi P.
    • Kyungpook Mathematical Journal
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    • v.58 no.4
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    • pp.651-675
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    • 2018
  • We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain sufficient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.