Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property in G_p metric spaces
Abstract
The purpose of this paper is to prove a general fixed point theorem for mappings involving almost altering distances and satisfying a new type of common limit range property in Gp metric spaces. In the last part of the paper, some fixed point results for mappings satisfying contractive conditions of integral type and for '-contractive mappings are obtained.
Keywords
fixed point; almost altering distance; common limit range property; G_p-metric spaces; implicit relation
References
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2. Abbas M., Rhoades B.E., Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. Comput. 215 (2009), no. 1, 262–269.
3. Ahmadi Zand M.R., Dehghan Nezhad A., A generalization of partial metric spaces, J. Contemp. Appl. Math. 1 (2011), no. 1, 86–93.
4. Ali J., Imdad M., An implicit function implies several contraction conditions, Sarajevo J. Math. 4(17) (2008), no. 2, 269–285.
5. Aydi H., Karapınar E., Salimi P., Some fixed point results in GP-metric spaces, J. Appl. Math. 2012, Art. ID 891713, 16 pp.
6. Barakat M.A., Zidan A.M., A common fixed point theorem for weak contractive maps in G_p-metric spaces, J. Egyptian. Math. Soc. 23 (2015), no. 2, 309–314.
7. Bilgili N., Karapınar E., Salimi P., Fixed point theorems for generalized contractions on GP-metric spaces, J. Inequal. Appl. 2013, 2013:39, 13 pp.
8. Branciari A., A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (2002), no. 9, 531–536.
9. Chi K.P., Karapınar E., Thanh T.D., A generalized contraction principle in partial metric spaces, Math. Comput. Modelling 55 (2012), no. 5–6, 1673–1681.
10. Ćirić L., Samet B., Aydi H., Vetro C., Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), no. 6, 2398–2406.
11. Dhage B.C., Generalised metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc. 84 (1992), no. 4, 329–336.
12. Dhage B.C., Generalized metric spaces and topological structure. I, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) 46 (2000), no. 1, 3–24 (2001).
13. Gülyaz S., Karapınar E., A coupled fixed point result in partially ordered partial metric spaces through implicit function, Hacet. J. Math. Stat. 42 (2013), no. 4, 347–357.
14. Gülyaz S., Karapınar E., Yüce İ.S., A coupled coincidence point theorem in partially ordered metric spaces with an implicit relation, Fixed Point Theory Appl. 2013, 2013:38, 11 pp.
15. Imdad M., Chauhan S., Employing common limit range property to prove unified metrical common fixed point theorems, Int. J. Anal. 2013, Art. ID 763261, 10 pp.
16. Imdad M., Chauhan S., Kadelburg Z., Fixed point theorem for mappings with common limit range property satisfying generalized (ψ,φ)-weak contractive conditions, Math. Sci. (Springer) 7 (2013), Art. 16, 8 pp.
17. Imdad M., Pant B.D., Chauhan S., Fixed point theorems in Menger spaces using (CLR_(ST)) property and applications, J. Nonlinear Anal. Optim. 3 (2012), no. 2, 225–237.
18. Imdad M., Sharma A., Chauhan S., Unifying a multitude of common fixed point theorems in symmetric spaces, Filomat 28 (2014), no. 6, 1113–1132.
19. Jungck G., Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771–779.
20. Jungck G., Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci. 4 (1996), no. 2, 199–215.
21. Kadelburg Z., Nashine H.K., Radenović S., Fixed point results under various contractive conditions in partial metric spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 107 (2013), no. 2, 241–256.
22. Karapınar E., Yüksel U., Some common fixed point theorems in partial metric spaces, J. Appl. Math. 2011, Art. ID 263621, 16 pp.
23. Karapınar E., Patel D.K., Imdad M., Gopal D., Some nonunique common fixed point theorems in symmetric spaces through CLR_(S,T) property, Int. J. Math. Math. Sci. (2013), Art. ID 753965, 8 pp.
24. Khan M.S., Swaleh M., Sessa S., Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30 (1984), no. 1, 1–9.
25. Kumar S., Chugh R., Kumar R., Fixed point theorem for compatible mappings satisfying a contractive condition of integral type, Soochow J. Math. 33 (2007), no. 2, 181–185.
26. Liu Y., Wu J., Li Z., Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci. 2005, no. 19, 3045–3055.
27. Matkowski J., Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc. 62 (1977), no. 2, 344–348.
28. Matthews S.G., Partial metric topology, in: Andima S. et al. (eds.), Papers on General Topology and Applications: Eighth Summer Conference at Queens College, New York Acad. Sci. 728, New York Academy of Sciences, New York, 1994, pp. 183–197.
29. Mustafa Z., Khandagji M., Shatanawi W., Fixed point results on complete G-metric spaces, Studia Sci. Math. Hungar. 48 (2011), no. 3, 304–319.
30. Mustafa Z., Obiedat H., A fixed point theorem of Reich in G-metric spaces, Cubo 12 (2010), no. 1, 83–93.
31. Mustafa Z., Obiedat H., Awawdeh F., Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl. 2008, Art. ID 189870, 12 pp.
32. Mustafa Z., Sims B., Some remarks concerning D-metric spaces, in: Falset J.G. et al. (eds.), Proceedings of the International Conference on Fixed Point Theory and Applications (Valencia, Spain, 2003), Yokohama Publ., Yokohama, 2004, pp. 189–198.
33. Mustafa Z., Sims B., A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006), no. 2, 287–297.
34. Mustafa Z., Sims B., Fixed point theorems for contractive mappings in complete Gmetric spaces, Fixed Point Theory Appl. 2009, Art. ID 917175, 10 pp.
35. Pant R.P., Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), no. 2, 436–440.
36. Pant R.P., Common fixed points of four mappings, Bull. Calcutta Math. Soc. 90 (1998), no. 4, 281–286.
37. Pant R.P., Common fixed point theorems for contractive maps, J. Math. Anal. Appl. 226 (1998), no. 1, 251–258.
38. Pant R.P., R-weak commutativity and common fixed points of noncompatible maps, Ganita 49 (1998), no. 1, 19–27.
39. Pant R.P., R-weak commutativity and common fixed points, Soochow J. Math. 25 (1999), no. 1, 37–42.
40. Parvaneh V., Roshan J.R., Kadelburg Z., On generalized weakly GP-contractive mappings in ordered GP-metric spaces, Gulf J. Math. 1 (2013), no. 1, 78–97.
41. Pathak H.K., Rodríguez-López R., Verma R.K., A common fixed point theorem using implicit relation and property (E.A) in metric spaces, Filomat 21 (2007), no. 2, 211–234.
42. Pathak H.K., Rodríguez-López R., Verma R.K., A common fixed point theorem of integral type using implicit relation, Nonlinear Funct. Anal. Appl. 15 (2010), no. 1, 1–12.
43. Popa V., Fixed point theorems for implicit contractive mappings, Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău 7 (1997), 127–133.
44. Popa V., Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), no. 1, 157–163.
45. Popa V., Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property, Filomat 31 (2017), no. 11, 3181–3192.
46. Popa V., Mocanu M., A new viewpoint in the study of fixed points for mappings satisfying a contractive condition of integral type, Bull. Inst. Politeh. Iaşi Secţ. Mat. Mec. Teor. Fiz. 53(57) (2007), no. 5, 269–286.
47. Popa V., Mocanu M., Altering distance and common fixed points under implicit relations, Hacet. J. Math. Stat. 38 (2009), no. 3, 329–337.
48. Popa V., Patriciu A.-M., A general fixed point theorem for mappings satisfying an φ-implicit relation in complete G-metric spaces, Gazi Univ. J. Sci. 25 (2012), no. 2, 403–408.
49. Popa V., Patriciu A.-M., A general fixed point theorem for pairs of weakly compatible mappings in G-metric spaces, J. Nonlinear Sci. Appl. 5 (2012), no. 2, 151–160.
50. Popa V., Patriciu A.-M., Two general fixed point theorems for pairs of weakly compatible mappings in G-metric spaces, Novi Sad J. Math. 42 (2012), no. 2, 49–60.
51. Popa V., Patriciu A.-M., A general fixed point theorem for a pair of self mappings with common limit range property in G-metric spaces, Facta Univ. Ser. Math. Inform. 29 (2014), no. 4, 351–370.
52. Popa V., Patriciu A.-M., Two general fixed point theorems for a sequence of mappings satisfying implicit relations in G_p-metric spaces, Appl. Gen. Topol. 16 (2015), no. 2, 225–231.
53. Popa V., Patriciu A.-M., Well posedness of fixed point problem for mappings satisfying an implicit relation in G_p-metric spaces, Math. Sci. Appl. E-Notes 3 (2015), no. 1, 108–117.
54. Rhoades B.E., Two fixed-point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 2003, no. 63, 4007–4013.
55. Sastry K.P.R., Babu G.V.R., Fixed point theorems in metric spaces by altering distances, Bull. Calcutta Math. Soc. 90 (1998), no. 3, 175–182.
56. Sastry K.P.R., Babu G.V.R., Some fixed point theorems by altering distances between the points, Indian J. Pure Appl. Math. 30 (1999), no. 6, 641–647.
57. Shatanawi W., Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces, Fixed Point Theory Appl. 2010, Art. ID 181650, 9 pp.
58. Sintunavarat W., Kumam P., Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math. 2011, Art. ID 637958, 14 pp.
59. Vetro C., Vetro F., Common fixed points of mappings satisfying implicit relations in partial metric spaces, J. Nonlinear Sci. Appl. 6 (2013), no. 3, 152–161.
2. Abbas M., Rhoades B.E., Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. Comput. 215 (2009), no. 1, 262–269.
3. Ahmadi Zand M.R., Dehghan Nezhad A., A generalization of partial metric spaces, J. Contemp. Appl. Math. 1 (2011), no. 1, 86–93.
4. Ali J., Imdad M., An implicit function implies several contraction conditions, Sarajevo J. Math. 4(17) (2008), no. 2, 269–285.
5. Aydi H., Karapınar E., Salimi P., Some fixed point results in GP-metric spaces, J. Appl. Math. 2012, Art. ID 891713, 16 pp.
6. Barakat M.A., Zidan A.M., A common fixed point theorem for weak contractive maps in G_p-metric spaces, J. Egyptian. Math. Soc. 23 (2015), no. 2, 309–314.
7. Bilgili N., Karapınar E., Salimi P., Fixed point theorems for generalized contractions on GP-metric spaces, J. Inequal. Appl. 2013, 2013:39, 13 pp.
8. Branciari A., A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (2002), no. 9, 531–536.
9. Chi K.P., Karapınar E., Thanh T.D., A generalized contraction principle in partial metric spaces, Math. Comput. Modelling 55 (2012), no. 5–6, 1673–1681.
10. Ćirić L., Samet B., Aydi H., Vetro C., Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), no. 6, 2398–2406.
11. Dhage B.C., Generalised metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc. 84 (1992), no. 4, 329–336.
12. Dhage B.C., Generalized metric spaces and topological structure. I, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) 46 (2000), no. 1, 3–24 (2001).
13. Gülyaz S., Karapınar E., A coupled fixed point result in partially ordered partial metric spaces through implicit function, Hacet. J. Math. Stat. 42 (2013), no. 4, 347–357.
14. Gülyaz S., Karapınar E., Yüce İ.S., A coupled coincidence point theorem in partially ordered metric spaces with an implicit relation, Fixed Point Theory Appl. 2013, 2013:38, 11 pp.
15. Imdad M., Chauhan S., Employing common limit range property to prove unified metrical common fixed point theorems, Int. J. Anal. 2013, Art. ID 763261, 10 pp.
16. Imdad M., Chauhan S., Kadelburg Z., Fixed point theorem for mappings with common limit range property satisfying generalized (ψ,φ)-weak contractive conditions, Math. Sci. (Springer) 7 (2013), Art. 16, 8 pp.
17. Imdad M., Pant B.D., Chauhan S., Fixed point theorems in Menger spaces using (CLR_(ST)) property and applications, J. Nonlinear Anal. Optim. 3 (2012), no. 2, 225–237.
18. Imdad M., Sharma A., Chauhan S., Unifying a multitude of common fixed point theorems in symmetric spaces, Filomat 28 (2014), no. 6, 1113–1132.
19. Jungck G., Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771–779.
20. Jungck G., Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci. 4 (1996), no. 2, 199–215.
21. Kadelburg Z., Nashine H.K., Radenović S., Fixed point results under various contractive conditions in partial metric spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 107 (2013), no. 2, 241–256.
22. Karapınar E., Yüksel U., Some common fixed point theorems in partial metric spaces, J. Appl. Math. 2011, Art. ID 263621, 16 pp.
23. Karapınar E., Patel D.K., Imdad M., Gopal D., Some nonunique common fixed point theorems in symmetric spaces through CLR_(S,T) property, Int. J. Math. Math. Sci. (2013), Art. ID 753965, 8 pp.
24. Khan M.S., Swaleh M., Sessa S., Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30 (1984), no. 1, 1–9.
25. Kumar S., Chugh R., Kumar R., Fixed point theorem for compatible mappings satisfying a contractive condition of integral type, Soochow J. Math. 33 (2007), no. 2, 181–185.
26. Liu Y., Wu J., Li Z., Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci. 2005, no. 19, 3045–3055.
27. Matkowski J., Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc. 62 (1977), no. 2, 344–348.
28. Matthews S.G., Partial metric topology, in: Andima S. et al. (eds.), Papers on General Topology and Applications: Eighth Summer Conference at Queens College, New York Acad. Sci. 728, New York Academy of Sciences, New York, 1994, pp. 183–197.
29. Mustafa Z., Khandagji M., Shatanawi W., Fixed point results on complete G-metric spaces, Studia Sci. Math. Hungar. 48 (2011), no. 3, 304–319.
30. Mustafa Z., Obiedat H., A fixed point theorem of Reich in G-metric spaces, Cubo 12 (2010), no. 1, 83–93.
31. Mustafa Z., Obiedat H., Awawdeh F., Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl. 2008, Art. ID 189870, 12 pp.
32. Mustafa Z., Sims B., Some remarks concerning D-metric spaces, in: Falset J.G. et al. (eds.), Proceedings of the International Conference on Fixed Point Theory and Applications (Valencia, Spain, 2003), Yokohama Publ., Yokohama, 2004, pp. 189–198.
33. Mustafa Z., Sims B., A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006), no. 2, 287–297.
34. Mustafa Z., Sims B., Fixed point theorems for contractive mappings in complete Gmetric spaces, Fixed Point Theory Appl. 2009, Art. ID 917175, 10 pp.
35. Pant R.P., Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), no. 2, 436–440.
36. Pant R.P., Common fixed points of four mappings, Bull. Calcutta Math. Soc. 90 (1998), no. 4, 281–286.
37. Pant R.P., Common fixed point theorems for contractive maps, J. Math. Anal. Appl. 226 (1998), no. 1, 251–258.
38. Pant R.P., R-weak commutativity and common fixed points of noncompatible maps, Ganita 49 (1998), no. 1, 19–27.
39. Pant R.P., R-weak commutativity and common fixed points, Soochow J. Math. 25 (1999), no. 1, 37–42.
40. Parvaneh V., Roshan J.R., Kadelburg Z., On generalized weakly GP-contractive mappings in ordered GP-metric spaces, Gulf J. Math. 1 (2013), no. 1, 78–97.
41. Pathak H.K., Rodríguez-López R., Verma R.K., A common fixed point theorem using implicit relation and property (E.A) in metric spaces, Filomat 21 (2007), no. 2, 211–234.
42. Pathak H.K., Rodríguez-López R., Verma R.K., A common fixed point theorem of integral type using implicit relation, Nonlinear Funct. Anal. Appl. 15 (2010), no. 1, 1–12.
43. Popa V., Fixed point theorems for implicit contractive mappings, Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău 7 (1997), 127–133.
44. Popa V., Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), no. 1, 157–163.
45. Popa V., Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property, Filomat 31 (2017), no. 11, 3181–3192.
46. Popa V., Mocanu M., A new viewpoint in the study of fixed points for mappings satisfying a contractive condition of integral type, Bull. Inst. Politeh. Iaşi Secţ. Mat. Mec. Teor. Fiz. 53(57) (2007), no. 5, 269–286.
47. Popa V., Mocanu M., Altering distance and common fixed points under implicit relations, Hacet. J. Math. Stat. 38 (2009), no. 3, 329–337.
48. Popa V., Patriciu A.-M., A general fixed point theorem for mappings satisfying an φ-implicit relation in complete G-metric spaces, Gazi Univ. J. Sci. 25 (2012), no. 2, 403–408.
49. Popa V., Patriciu A.-M., A general fixed point theorem for pairs of weakly compatible mappings in G-metric spaces, J. Nonlinear Sci. Appl. 5 (2012), no. 2, 151–160.
50. Popa V., Patriciu A.-M., Two general fixed point theorems for pairs of weakly compatible mappings in G-metric spaces, Novi Sad J. Math. 42 (2012), no. 2, 49–60.
51. Popa V., Patriciu A.-M., A general fixed point theorem for a pair of self mappings with common limit range property in G-metric spaces, Facta Univ. Ser. Math. Inform. 29 (2014), no. 4, 351–370.
52. Popa V., Patriciu A.-M., Two general fixed point theorems for a sequence of mappings satisfying implicit relations in G_p-metric spaces, Appl. Gen. Topol. 16 (2015), no. 2, 225–231.
53. Popa V., Patriciu A.-M., Well posedness of fixed point problem for mappings satisfying an implicit relation in G_p-metric spaces, Math. Sci. Appl. E-Notes 3 (2015), no. 1, 108–117.
54. Rhoades B.E., Two fixed-point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 2003, no. 63, 4007–4013.
55. Sastry K.P.R., Babu G.V.R., Fixed point theorems in metric spaces by altering distances, Bull. Calcutta Math. Soc. 90 (1998), no. 3, 175–182.
56. Sastry K.P.R., Babu G.V.R., Some fixed point theorems by altering distances between the points, Indian J. Pure Appl. Math. 30 (1999), no. 6, 641–647.
57. Shatanawi W., Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces, Fixed Point Theory Appl. 2010, Art. ID 181650, 9 pp.
58. Sintunavarat W., Kumam P., Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math. 2011, Art. ID 637958, 14 pp.
59. Vetro C., Vetro F., Common fixed points of mappings satisfying implicit relations in partial metric spaces, J. Nonlinear Sci. Appl. 6 (2013), no. 3, 152–161.
PopaV., & PatriciuA.-M. (2018). Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property in G_p metric spaces. Annales Mathematicae Silesianae, 32, 295-312. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13928
Valeriu Popa
“Vasile Alecsandri” University of Bacău, Romania Romania
“Vasile Alecsandri” University of Bacău, Romania Romania
Alina-Mihaela Patriciu
Alina.Patriciu@ugal.ro
Department of Mathematics and Computer Sciences, Faculty of Sciences and Environment, “Dunărea de Jos” University of Galați, Romania Romania
Department of Mathematics and Computer Sciences, Faculty of Sciences and Environment, “Dunărea de Jos” University of Galați, Romania Romania
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