본문 바로가기
KERD
논문KCI 등재

Common coupled fixed point results for hybrid pair of mapping under generalized (ψ, θ, ϕ)-contraction with application

Amrish Handa
한국수학교육학회|2019.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제26권 제3호|pp. 111-131|DOI https://doi.org/10.7468/jksmeb.2019.26.3.111

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

coupled coincidence pointcoupled fixed pointF-weakly commutingintegral equation.w-compatibilitygeneralized (𝜓𝜃𝜑)-contraction
주제분류수학

초록

We introduce (CLRg) property for hybrid pair F : X×X→2^X and g : X→X. We also introduce joint common limit range (JCLR) property for two hybrid pairs F,G : X×X→2^X and f, g : X→X. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (𝜓,𝜃,𝜑)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

Abstract

We introduce (CLRg) property for hybrid pair F : X×X→2^X and g : X→X. We also introduce joint common limit range (JCLR) property for two hybrid pairs F,G : X×X→2^X and f, g : X→X. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (𝜓,𝜃,𝜑)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

참고문헌 (32)

  1. M. Abbas, "Coupled coincidence point and common xed point theorems for hybrid pair of mappings", Fixed Point Theory Appl, pp.4~ (2012)
  2. M.A. Ahmed, "Common fixed point theorems for hybrid pairs of maps in fuzzy metric spaces", J. Egyptian Math. Soc (2013)
  3. A. Alotaibi, "Coupled coincidence points for monotone operators in partially ordered metric spaces", Fixed Point Theory Appl, pp.44~ (2011)
  4. S.M. Alsulami, "Some coupled coincidence point theorems for a mixed monotone opera-tor in a complete metric space endowed with a partial order by using altering distance functions", Fixed Point Theory Appl, pp.194~ (2013)
  5. T.G. Bhaskar, "Fixed point theorems in partially ordered metric spaces and applications", Nonlinear Anal, 65(7), pp.1379~1393 (2006)
  6. S. Chauhan, "Common Fixed point theorems for weakly compatible mappings in fuzzy metric spaces using (JCLR) property", Applied Mathe-matics, 3, pp.976~982 (2012)
  7. B. Deshpande, "Nonlinear mixed monotone-generalized contractions on partially ordered modi ed intuitionistic fuzzy metric spaces with application to integral equations", Afr. Mat, 26(3-4), pp.317~343 (2015)
  8. B. Deshpande, "Application of coupled xed point technique in solving integral equations on modified intuitionistic fuzzy metric spaces", Adv. Fuzzy Syst (2014)
  9. B. Deshpande, "Common coupled fixed point theorems for hybrid pair of mappings satisfying an implicit relation with application", Afr. Mat, 27(1-2), pp.149~167 (2016)
  10. B. Deshpande, "Common coupled fixed point theorems for two hybrid pairs of mappings under φ - φ contraction", ISRN (2014)
  11. Bhavana Deshpande, "Common coupled fixed point for hybrid pair of mappings under generalized nonlinear contraction", East Asian Mathematical Journal, 31(1), pp.77~89 (2015), 영남수학회[DOI]
  12. B. Deshpande, "Common coupled fixed point theorems for hybrid pair of mappings under some weaker conditions satisfying an implicit relation", Nonlinear Analysis Forum, 20, pp.79~93 (2015)
  13. B. Deshpande, "Common coupled fixed point theorems for two hybrid pairs of mappings satis-fying an implicit relation", Sarajevo J. Math, 11(23), pp.85~100 (2015)
  14. Bhavana Deshpande, "COMMON COUPLED FIXED POINT THEOREM UNDER GENERALIZED MIZOGUCHI-TAKAHASHI CONTRACTION FOR HYBRID PAIR OF MAPPINGS GENERALIZED MIZOGUCHI-TAKAHASHI CONTRACTION", 순수 및 응용수학, 22(3), pp.199~214 (2015), 한국수학교육학회
  15. D. Guo, "Coupled fixed points of nonlinear operators with ap-plications", Nonlinear Anal, 11(5), pp.623~632 (1987)
  16. J. Harjani, "Fixed point theorems for mixed monotone operators and applications to integral equations", Nonlinear Anal, 74, pp.1749~1760 (2011)
  17. J. Harjani, "Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations", Nonlinear Anal, 72(3-4), pp.1188~1197 (2010)
  18. M.A. Khan Sumitra, "CLRg property for coupled fixed point theorems in fuzzy metric spaces", Int. J. Appl. Phy. Math, 2(5), pp.355~358 (2012)
  19. V. Lakshmikantham, "Coupled fixed point theorems for nonlinear contrac-tions in partially ordered metric spaces", Nonlinear Anal, 70(12), pp.4341~4349 (2009)
  20. W. Long, "Some coupled coincidence and common fixed point results for hybrid pair of mappings in 0-complete partial metric spaces", Fixed Point Theory Appl, pp.145~ (2013)
  21. N.V. Luong, "Coupled fixed points in partially ordered metric spaces and application", Nonlinear Anal, 74, pp.983~992 (2011)
  22. J.T. Markin, "Continuous dependence of fixed point sets", Proc. Amer. Math. Soc, 38, pp.545~547 (1947)
  23. S.B. Nadler, "Multivalued contraction mappings", Pacific J. Math, 30, pp.475~488 (1969)
  24. J.J. Nieto, "Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations", Order, 22, pp.223~239 (2005)
  25. M.C.B. Reurings, "A fixed point theorem in partially ordered sets and some applications to matrix equations", Proc. Amer. Math. Soc, 132, pp.1435~1443 (2004)
  26. A. Razani, "Coupled coincidence point results for ( ; ; )-weak con-tractions in partially ordered metric spaces", J. Appl. Math (2012)
  27. J. Rodriguez-Lopez, "The Hausdorff fuzzy metric on compact sets", Fuzzy Sets Syst, 147, pp.273~283 (2004)
  28. B. Samet, "Discussion on some coupled fixed point theorems", Fixed Point Theory Appl, pp.50~ (2013)
  29. F. Shaddad, "Coupled point results in partially ordered metric spaces without compatibility", Fixed Point Theory Appl, pp.204~ (2014)
  30. N. Singh, "Coupled coincidence and common fixed point theorems for set-valued and single-valued mappings in fuzzy metric space", Journal of Fuzzy Set Valued Analysis (2012)
  31. W. Sintunavarat, "Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces", Journal of Applied Mathematics (2011)
  32. W. Sintunavarat, "Coupled fixed point theorems for nonlinear contractions without mixed monotone property", Fixed Point Theory Appl, pp.170~ (2012)

관련 논문AI추천

COMMON COUPLED FIXED POINT THEOREM UNDER GENERALIZED MIZOGUCHI-TAKAHASHI CONTRACTION FOR HYBRID PAIR OF MAPPINGS GENERALIZED MIZOGUCHI-TAKAHASHI CONTRACTIONAmrish Handa, Bhavana Deshpande한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제3호Common coupled fixed point for hybrid pair of mappings under generalized nonlinear contractionAmrish Handa, Bhavana Deshpande영남수학회 · East Asian Mathematical Journal2015 · 제31권 제1호EMPLOYING α-ψ-CONTRACTION TO PROVE COUPLED COINCIDENCE POINT THEOREM FOR GENERALIZED COMPATIBLE PAIR OF MAPPINGS ON PARTIALLY ORDERED METRIC SPACESAmrish Handa, Bhavana Deshpande한국수학교육학회 · 이론수학과 교직수학2018 · 제25권 제2호COUPLED COINCIDENCE POINT RESULTS FOR GENERALIZED SYMMETRIC MEIR-KEELER CONTRACTION ON PARTIALLY ORDERED METRIC SPACES WITH APPLICATIONAmrish Handa, Bhavana Deshpande한국수학교육학회 · 이론수학과 교직수학2017 · 제24권 제2호Coupled fixed point theorems for rational inequality in generalized metric spacesDeepak Singh, M.S.Rathore, Surjeet Singh Tomar, Varsha Chauhan영남수학회 · East Asian Mathematical Journal2015 · 제31권 제1호EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED GERAGHTY-TYPE CONTRACTION WITH APPLICATIONAmrish Handa한국수학교육학회 · 이론수학과 교직수학2020 · 제27권 제3호

이 간행물의 다른 논문 (6건)

NORTH KOREA NUCLEAR CRISIS; POLICIES AND STRATEGIESNader Asghari, Madjid Eshaghi Gordjipp. 133-156GENERALIZED SECOND-ORDER DIFFERENTIAL EQUATIONS WITH TWO-POINT BOUNDARY CONDITIONSYoung Jin Kimpp. 157-175EXTREMAL CHEMICAL TREES WITH RESPECT TO HYPER-ZAGREB INDEXAli Reza Ashrafi, Ali Ghalavand, Reza Sharafdini, Ottorino Oripp. 177-188SOME INEQUALITIES FOR THE WEIGHTED CHAOTICALLY GEOMETRIC MEANSilvestru Sever Dragomirpp. 189-197INSERTION OF A CONTRA-BAIRE-1 (BAIRE-.5) FUNCTIONMajid Mirmiran, Binesh Naderipp. 199-208
원문 보기