• Title/Summary/Keyword: B-contraction

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APPLICATION OF CONTRACTION MAPPING PRINCIPLE IN INTEGRAL EQUATION

  • Amrish Handa
    • The Pure and Applied Mathematics
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    • v.30 no.4
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    • pp.443-461
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    • 2023
  • In this paper, we establish some common fixed point theorems satisfying contraction mapping principle on partially ordered non-Archimedean fuzzy metric spaces and also derive some coupled fixed point results with the help of established results. We investigate the solution of integral equation and also give an example to show the applicability of our results. These results generalize, improve and fuzzify several well-known results in the recent literature.

An ergonomicstudy on the function of sleeve - On the expansion and contraction of skin surface of the upper extremity - (Sleeve의 기능성에 관한 인간공학적 연구)

  • 박영득
    • Journal of the Korean Home Economics Association
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    • v.23 no.3
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    • pp.1-8
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    • 1985
  • This study is an ergonomic study on the function of sleeves related with the expansion and contraction of the upper Extremity skin surface by various movememts. RESULTS : 1. According to the plane figure, a. The change of form is like fig. 3. b. In the changing rates of the expansion and contraction of skin surface by various movements, that of arm hole girth shows an extremely big discrepancy and that of Elbow Girth shows a relative low one. c. According to the rate of the expansion and contraction of each block, the inside of the upper arm area expands most in all the blocks measured. 2. According to the rate of expansion and contraction of skin surface by somatometry, inside lehgth of arm in M\sub 2\ and outside length of the upper arm in M\sub 4\ expand significantly8and also elbow girth in M\sub 6\, M\sub 7\, M\sub 8\ expands significantly.

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FIXED POINT THEOREMS FOR (𝜙, F)-CONTRACTION IN GENERALIZED ASYMMETRIC METRIC SPACES

  • Rossafi, Mohamed;Kari, Abdelkarim;Lee, Jung Rye
    • The Pure and Applied Mathematics
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    • v.29 no.4
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    • pp.369-399
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    • 2022
  • In the last few decades, a lot of generalizations of the Banach contraction principle have been introduced. In this paper, we present the notion of (𝜙, F)-contraction in generalized asymmetric metric spaces and we investigate the existence of fixed points of such mappings. We also provide some illustrative examples to show that our results improve many existing results.

REICH-TYPE CONTRACTION ON EXTENDED METRIC SPACE OF TYPE (φ, ρ) AND SOME FIXED POINT RESULTS

  • Asma Souaiaia;Wasfi Shatanawi;Abdalla Ahmad Tallafha
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.3
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    • pp.719-729
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    • 2023
  • In this article, we present a new notion called "extended metric spaces of type (φ, ρ)" as a generalization of extended b-metric spaces. Also, we establish a fixed point result of a Reich-type contraction on an extended metric space of type (φ, ρ). We also provide several examples to demonstrate the significance of the established results.

A Study on Easing contraction made by different angles(Part II) -About variations of sleeve cap curve lines- (재단각도 변화에 따른 오그림에 관한 연구 (제 2보) -소매산높이에 따른 각도변화를 중심으로-)

  • 이명희
    • Journal of the Korean Society of Clothing and Textiles
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    • v.23 no.3
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    • pp.353-360
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    • 1999
  • An investigation made of the variations of angle of bias on the top of the sleeve cap curve line and calculated easing contraction ratio by capheights(A ; a,h$\times$5,/6) B: A, H/4 +4cm C:A.H/3 D: A.H/ 4+3cm E:AH/4+2cm, F: A,H/4+1cm, G: A,H/4, H:A,H/6, I:A,H/8) and the efects of easing contraction on the cap curve lines of sleeve A, D, G by easing stitch density with the gathering foot: sewing condition-lockstitch industrial machine stitch density(N1.0 ; 38stitches/3cm N1.5: 26stitches/3cm, N2.0 ; 19stitches/3cm, N2.5 ; 14stitches/ 3cm) The results obtained were as follows; 1) The variations of the angle of bias on the top of the sleeve cap curve line by cap heights can be done according to the angle balance (front; $\alpha$-$\beta$ back ; $\alpha$'- $\beta$') between the angle (front ;$\alpha$, $\beta$, back ; $\alpha$'- $\beta$') of bias of the two base-lines. 2) The higher cap height the more higher the calculated easing contraction ratio. 3) The lower the stitch density the higher easing contraction ratio. 4) The effects of easing contraction was that sleeve G was more than sleeve A, D.

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COUPLED COINCIDENCE POINT RESULTS FOR GENERALIZED SYMMETRIC MEIR-KEELER CONTRACTION ON PARTIALLY ORDERED METRIC SPACES WITH APPLICATION

  • Deshpande, Bhavana;Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.24 no.2
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    • pp.79-98
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    • 2017
  • We establish a coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X{\times}X{\rightarrow}X$ under generalized symmetric Meir-Keeler contraction on a partially ordered metric space. We also deduce certain coupled fixed point results without mixed monotone property of $F:X{\times}X{\rightarrow}X$. An example supporting to our result has also been cited. As an application the solution of integral equations are obtain here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.

EMPLOYING α-ψ-CONTRACTION TO PROVE COUPLED COINCIDENCE POINT THEOREM FOR GENERALIZED COMPATIBLE PAIR OF MAPPINGS ON PARTIALLY ORDERED METRIC SPACES

  • Deshpande, Bhavana;Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.25 no.2
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    • pp.73-94
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    • 2018
  • We introduce some new type of admissible mappings and prove a coupled coincidence point theorem by using newly defined concepts for generalized compatible pair of mappings satisfying ${\alpha}-{\psi}$ contraction on partially ordered metric spaces. We also prove the uniqueness of a coupled fixed point for such mappings in this setup. Furthermore, we give an example and an application to integral equations to demonstrate the applicability of the obtained results. Our results generalize some recent results in the literature.