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Application of Generalized Weak Contraction in Integral Equation

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초록

This manuscript is divided into three segments. In the first segment, we prove a unique common fixed point theorem satisfying generalized weak contraction on partially ordered metric spaces and also give an example to support our results presented here. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of integral equation as an application. Our results generalize, extend and improve several well-known results of the existing literature.

Abstract

This manuscript is divided into three segments. In the first segment, we prove a unique common fixed point theorem satisfying generalized weak contraction on partially ordered metric spaces and also give an example to support our results presented here. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of integral equation as an application. Our results generalize, extend and improve several well-known results of the existing literature.

참고문헌 (21)

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  4. Binayak S. Choudhury, "(ψ,α,β)-weak contractions in partially ordered met-ric spaces", Applied Mathematics Letters, 25(1), pp.6~10 (2012), Elsevier BV[DOI]
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  8. Bhavana Deshpande, "UTILIZING ISOTONE MAPPINGS UNDER GERAGHTY-TYPE CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION", 순수 및 응용수학, 25(4), pp.279~295 (2018), 한국수학교육학회[DOI]
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  10. Bhavana Deshpande, "HUGE CONTRACTION ON PARTIALLY ORDERED METRIC SPACES", 순수 및 응용수학, 23(1), pp.35~51 (2016), 한국수학교육학회
  11. Bhavana Deshpande, "EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED NONLINEAR CONTRACTION WITH APPLICATIONS", East Asian Mathematical Journal, 32(3), pp.333~354 (2016), 영남수학회[DOI]
  12. İnci M Erhan, "Remarks on ‘Coupled coincidence point results for a generalized compatible pair with applications’", Fixed Point Theory and Applications, 2014(1), pp.207~ (2014), Springer Science and Business Media LLC[DOI]
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  16. J. Harjani, "Fixed point theorems for mixed monotone operators and applications to integral equations", Nonlinear Analysis: Theory, Methods & Applications, 74(5), pp.1749~1760 (2011), Elsevier BV[DOI]
  17. Nawab Hussain, "Coupled coincidence point results for a generalized compatible pair with applications", Fixed Point Theory and Applications, 2014(1), pp.62~ (2014), Springer Science and Business Media LLC[DOI]
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  19. V. Lakshmikantham, "Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces", Nonlinear Analysis: Theory, Methods & Applications, 70(12), pp.4341~4349 (2009), Elsevier BV[DOI]
  20. Nguyen Van Luong, "Coupled fixed points in partially ordered metric spaces and application", Nonlinear Analysis: Theory, Methods & Applications, 74(3), pp.983~992 (2011), Elsevier BV[DOI]
  21. Bessem Samet, "Discussion on some coupled fixed point theorems", Fixed Point Theory and Applications, 2013(1), pp.50~ (2013), Springer Science and Business Media LLC[DOI]

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