Connecting various types of cyclic contractions and contractive self-mappings with Hardy-Rogers self-mappings

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• 作者：Panda Sumati Kumari ; Dinesh Panthi
• 关键词：47H10 ; 54H25 ; modified Hardy ; Rogers cyclic contraction ; Hardy ; Rogers cyclic orbital contraction ; Hardy ; Rogers F ; contraction ; generating space of b ; dislocated metric family ; b ; dislocated metric ; dislocated metric ; fixed point
• 刊名：Fixed Point Theory and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,669 KB
• 参考文献：1. Banach, S: Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fundam. Math. 3, 133-181 (1922) MATH
  2. Kannan, R: Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76 (1968) MathSciNet MATH
  3. Reich, S: Some remarks concerning contraction mappings. Can. Math. Bull. 14, 121-124 (1971) CrossRef MATH
  4. Chatterjea, SK: Fixed-point theorems. C. R. Acad. Bulg. Sci. 25, 727-730 (1972) MathSciNet MATH
  5. Ćirić, LB: Generalized contractions and fixed-point theorems. Publ. Inst. Math. (Belgr.) 12(26), 19-26 (1971)
  6. Hardy, GE, Rogers, TD: A generalization of a fixed point theorem of Reich. Can. Math. Bull. 16, 201-206 (1973) MathSciNet CrossRef MATH
  7. Subrahmanyam, PV: Completeness and fixed-points. Monatshefte Math. 80, 325-330 (1975) MathSciNet CrossRef MATH
  8. Kannan, R: Some results on fixed points. II. Am. Math. Mon. 76, 405-408 (1969) CrossRef MATH
  9. Rhodes, BE, Sessa, S, Khan, MS, Khan, MD: Some fixed point theorems for Hardy Rogers type mappings. Int. J. Math. Math. Sci. 7(1), 75-87 (1984) CrossRef
  10. Abbas, M, Aydi, H, Radenović, S: Fixed point of Hardy-Rogers contractive mappings in partially ordered partial metric spaces. Int. J. Math. Math. Sci. 2012, Article ID 313675 (2012). doi:10.​1155/​2012/​313675 CrossRef
  11. Kumari, PS, Kumar, VV, Sarma, R: New version for Hardy and Rogers type mapping in dislocated metric space. Int. J. Basic Appl. Sci. 1(4), 609-617 (2012)
  12. Kirk, WA, Srinavasan, PS, Veeramani, P: Fixed points for mapping satisfying cyclical contractive conditions. Fixed Point Theory 4, 79-89 (2003) MathSciNet MATH
  13. Mongkolkeha, C, Kumam, P: Best proximity point theorems for generalized cyclic contractions in ordered metric spaces. J. Optim. Theory Appl. 155, 215-226 (2012) MathSciNet CrossRef MATH
  14. Sintunavarat, W, Kumam, P: Common fixed point theorem for cyclic generalized multi-valued contraction mappings. Appl. Math. Lett. 25(11), 1849-1855 (2012) MathSciNet CrossRef MATH
  15. Nashine, HK, Pathak, RP, Somvanshi, PS, Pantelic, S, Kumam, P: Solutions for a class of nonlinear Volterra integral and integro-differentialequation using cyclic \((\varphi,\psi,\theta)\) -contraction. Adv. Differ. Equ. 2013, 106 (2013) MathSciNet CrossRef
  16. Zoto, K, Kumari, PS, Hoxha, E: Some fixed point theorems and cyclic contractions in dislocated and dislocated quasi-metric spaces. Am. J. Numer. Anal. 2(3), 79-84 (2014)
  17. Radenović, S: Some remarks on mappings satisfying cyclical contractive conditions. Afr. Math. (2015). doi:10.​1007/​s13370-015-0339-2
  18. Abbas, M, Nazir, T, Gopal, D: Common fixed point results for generalized cyclic contraction mappings. Afr. Math. 26(1), 265-273 (2015) MathSciNet CrossRef MATH
  19. Radenović, S, Dosenović, T, Lampert, TA, Golubović, Z: A note on some recent fixed point results for cyclic contractions in b-metric spaces and an application to integral equations. Appl. Math. Comput. 273, 155-164 (2016) MathSciNet CrossRef
  20. Karpagam, S, Agrawal, S: Best proximity points theorems for cyclic Meir-Keeler contraction maps. Nonlinear Anal. 74, 1040-1046 (2011) MathSciNet CrossRef MATH
  21. Zlatanov, B: Best proximity points for p-summing cyclic orbital Meir-Keeler contractions. Nonlinear Anal., Model. Control 20(4), 528-544 (2015) MathSciNet
  22. Karapınar, E, Ramaguera, S, Kenan, T: Fixed points for cyclic orbital generalized contractions on complete metric spaces. Cent. Eur. J. Math. 11(3), 552-560 (2013) MathSciNet MATH
  23. Wardowski, D: Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012, Article ID 94 (2012) MathSciNet CrossRef
  24. Shukla, S, Radenović, S: Some common fixed point theorems for F-contraction type mappings in 0-complete partial metric spaces. J. Math. 2013, Article ID 878730 (2013)
  25. Minak, G, Helvaci, A, Altun, I: Ćirić type generalized F-contractions on complete metric spaces and fixed point results. Filomat 28(6), 1143-1151 (2014) MathSciNet CrossRef
  26. Kumari, PS, Zoto, K, Panthi, D: d-Neighborhood system and generalized F-contraction in dislocated metric space. SpringerPlus 4(1), 1-10 (2015) CrossRef
  27. Sedghi, S, Shobe, N, Aliouche, A: A generalization of fixed point theorems in S-metric spaces. Mat. Vesn. 64(3), 258-266 (2012) MathSciNet MATH
  28. Azam, A, Fisher, B, Khan, M: Common fixed point theorems in complex valued metric spaces. Numer. Funct. Anal. Optim. 32(3), 243-253 (2011) MathSciNet CrossRef MATH
  29. Abbas, et al.: Generalized coupled common fixed point results in partially ordered A-metric spaces. Fixed Point Theory Appl. 2015, Article ID 64 (2015) CrossRef
  30. Sarma, IR, Rao, JM, Kumari, PS, Panthi, D: Convergence axioms on dislocated symmetric spaces. Abstr. Appl. Anal. 2014, Article ID 745031 (2014). doi:10.​1155/​2014/​7450317 CrossRef
  31. Kumari, PS, Ramana, CV, Zoto, K: On quasi-symmetric space. Indian J. Sci. Technol. 7(10), 1583-1587 (2014)
  32. Kumari, PS, Sarma, IR, Rao, JM: Metrization theorem for a weaker class of uniformities. Afr. Math. (2015). doi:10.​1007/​s13370-015-0369-9 MATH
  33. Kumari, PS, Panthi, D: Cyclic contractions and fixed point theorems on various generating spaces. Fixed Point Theory Appl. 2015, Article ID 153 (2015) MathSciNet CrossRef
  34. Sarma, IR, Kumari, PS: On dislocated metric spaces. Int. J. Math. Arch. 3(1), 7-27 (2012)
  35. Kumari, PS, et al.: Common fixed point theorems on weakly compatible maps on dislocated metric spaces. Math. Sci. 6, 71 (2012) MathSciNet CrossRef
  36. Kumari, PS: On dislocated quasi metrics. J. Adv. Stud. Topol. 3(2), 66-74 (2012) MathSciNet CrossRef
  37. Panthi, D, Jha, K, Jha, PK, Kumari, PS: A common fixed point theorem for two pairs of mappings in dislocated metric space. Am. J. Comput. Math. 5, 106-112 (2015) CrossRef
  38. Kumari, PS, Ramana, CV, Zoto, K, Panthi, D: Fixed point theorems and generalizations of dislocated metric spaces. Indian J. Sci. Technol. 8(S3), 154-158 (2015) CrossRef
  39. Panthi, D: Common fixed point theorems for compatible mapping in dislocated metric space. Int. J. Math. Anal. 9(45), 2235-2242 (2015)
  40. Zoto, K, Isufati, A, Kumari, PS: Fixed point results and E.A-property in dislocated and dislocated quasi-metric spaces. Turk. J. Anal. Number Theory 3(1), 24-29 (2015)
  
• 作者单位：Panda Sumati Kumari (1)
  Dinesh Panthi (2)
  
  1. Department of Mathematics, National Institute of Technology, Andhra Pradesh, AP, India
  2. Department of Mathematics, Nepal Sanskrit University, Valmeeki campus, Exhibition road, Kathmandu, Nepal
  
• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

In this paper, we introduce the new classes of Hardy-Rogers type cyclic contractions and prove pertinent fixed point theorems for these Hardy-Rogers type contractions in the generating space of a b-dislocated metric family. Keywords modified Hardy-Rogers cyclic contraction Hardy-Rogers cyclic orbital contraction Hardy-Rogers F-contraction generating space of b-dislocated metric family b-dislocated metric dislocated metric fixed point