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Year 2015, Volume: 3 Issue: 1, 108 - 117, 15.05.2015

Valeriu Popa , Alina-mihaela Patrıcıu

https://doi.org/10.36753/mathenot.421226
Cited By: 2

Abstract

References

  • [1] Abbas, M., Nazi, T., Radanovi´c, S., Some periodic point results in generalized metric spaces. Appl. Math. Comput. 217 (2010), 4084-4099.
  • [2] Abdeljawad, T., Karapinar, E., Tas, K., Existence and uniqueness of a common fixed point on partial metric spaces. Appl. Math. Lett. 24 (2011), no. 11, 1900-1904.
  • [3] Akkouchi, M., Popa, V., Well posedness of common fixed point problem for three mappings under strict contractive conditions. Bul. Univ. Petrol - Gaze Ploie¸sti, Ser. Mat. Inform. Fiz. 61 (2009), no. 2, 1-10.
  • [4] Akkouchi, M., Popa, V., Well posedness of a fixed point problem using G - functions. Sci. Stud. Res. Ser. Math. Inform. 20 (2010), 5-12.
  • [5] Akkouchi, M., Popa, V., Well posedness of a fixed point problem for mappings satisfying an implicit relation. Demonstr. Math. 43 (2010), no. 4, 923-929.
  • [6] Akkouchi, M., Popa, V., Well posedness of fixed point problem for hybrid pairs of mappings. Fasc. Math. 46 (2011), 5-16.
  • [7] Altun, I., Sola, F., Simsek, H., Generalized contractions on partial metric spaces. Topology Appl. 157 (2010), no. 18, 2778-2785.
  • [8] Aydi, H., Karapinar, E., Salimi, P., Some fixed point results in Gp-metric spaces. J. Appl. Math. (2012), Article ID 891713.
  • [9] Barakat, M. A., Zidan, A. M., A common fixed point theorem for weak contractive maps in Gp - metric spaces. J. Egyptian Math. Soc. (2014), DOI: 10.1016/j.joems.2014.06.008.
  • [10] Bilgili, N., Karapinar, E., Salimi, P., Fixed point theorems for generalized contractions on Gp - metric spaces. J. Inequalities and Appl. Math.(2013), 2013:39.
  • [11] Chi, R., Karapinar, E., Thanh, T. D., A generalized contraction principle in partial metric spaces. Math. Comput. Modelling 55 (2012), no. 5 - 6, 1673-1681.
  • [12] De Blasi, F. S., Myjak, J., Sur la porosit´e de l’ensemble des contractions sans point fixe. Comptes Rend. Acad. Sci. Paris 308 (1989), 51-54.
  • [13] Dhage, B. C., Generalized metric spaces and mappings with fixed point. Bull. Calcutta Math. Soc. 84 (1992), 329-336.
  • [14] Dhage, B. C., Generalized metric spaces and topological structures I. An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si, Mat. 46 (2000), 3-24.
  • [15] Kadelburg, Z., Nashine, H. K., Radanovic S., Fixed point results under various contractive conditions in partial metric spaces. RACSAM 10 (2013), 241-256.
  • [16] Karapinar, E., Erhan, I. M., Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett. 24 (2011), no. 11, 1900-1904.
  • [17] Kaushal, D. S., Pogey, S. S., Some results of fixed point theorems on complete G - metric spaces. South Asian J. Math. 2 (2014), no. 4, 318-324.
  • [18] Lahiri, B. K., Das, P., Well-posedness and porosity of certain classes of operators. Demonstr. Math. 38 (2005), 170-176.
  • [19] Matthews, S., Partial metric topology and applications. Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728 (1994), 183-197.
  • [20] Mohanta, S., K., Some fixed point theorems in G - metric spaces. An. S¸t. Univ. Ovidius Constant¸a, Ser. Mat. 20 (2012), no. 1, 285-306.
  • [21] Mustafa, Z., Khandagji, M., Shatanawi, W., Fixed point results on complete G - metric spaces. St. Sci. Math. Hungarica 48 (2011), no. 3, 304-319.
  • [22] Mustafa, Z., Obiedat, H., A fixed point theorem of Reich in G - metric spaces. Cubo Math. J. 12 (2010), no. 1, 83-93.
  • [23] Mustafa, Z., Obiedat, H., Awawdeh, F. Some fixed point theorem for mapping on complete G - metric spaces. Fixed Point Theory Appl. (2008), Article ID 189870.
  • [24] Mustafa, Z., Shatanawi, W., Bataineh, M., Existence of fixed point results in G - metric spaces. Intern. J. Math. Math. Sci. (2009), Article ID 283028.
  • [25] Mustafa, Z., Sims, B., Some remarks concerning D - metric spaces. Conf. Fixed Point Theory Appl., Yokohama (2004), 184-198.
  • [26] Mustafa, Z., Sims, B., A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 7 (2006), no. 2, 289-297.
  • [27] Mustafa, Z., Sims, B., Fixed point theorems for contractive mappings in complete G - metric spaces. Fixed Point Theory Appl. (2009), Article ID 917175.
  • [28] Parvaneh, V., Roshan, J. R., Kadelburg, Z., On generalized weakly GP-contractive mappings in ordered GP-metric spaces, Gulf J. Math. 1 (2013), 78-97.
  • [29] Popa, V., Fixed point theorems for implicit contractive mappings. Stud. Cercet. S¸tiint¸., Ser. Mat., Univ. Bac˘au 7 (1997), 129-133.
  • [30] Popa, V., Some fixed point theorems for compatible mappings satisfying an implicit relation. Demonstr. Math. 32 (1999), 157-163.
  • [31] Popa, V., Well posedness of fixed point problem in orbitally complete metric spaces. Stud. Cercet. S¸tiint¸., Ser. Mat., Univ. Bac˘au 16, Suppl. (2006), 209-214.
  • [32] Popa, V., Well posedness of fixed point problem in compact metric spaces. Bul. Univ. Petrol - Gaze Ploie¸sti, Ser. Mat. Inform. Fiz. 60 (2008), no. 1, 1-4.
  • [33] Popa, V., A general fixed point theorem for several mappings in G - metric spaces. Sci. Stud. Res., Ser. Math. Inform. 21 (2011), no. 1, 205-214.
  • [34] 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.
  • [35] 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.
  • [36] Popa, V., Patriciu, A.-M., A general fixed point theorem for pair of weakly compatible mappings in G - metric spaces. J. Nonlinear Sci. Appl. 5 (2012), 151-160.
  • [37] Popa, V., Patriciu, A.-M., Fixed point theorems for mappings satisfying an implicit relation in complete G - metric spaces. Bul. Inst. Politehn. Ia¸si, Ser. Mat. Mec. Teor. Fiz. 59 (63) (2013), 97-123.
  • [38] Reich, S., Zaslavski, A. J., Well posedness of fixed point problem. Far East J. Math. Special Volume, Part III (2001), 393-401.
  • [39] Shatanawi, W., Fixed point theory for contractive mappings satisfying ϕ - maps in G - metric spaces. Fixed Point Theory Appl. (2010), Article ID 181650.
  • [40] Shatanawi, W., Common fixed point results for two self - maps in G - metric spaces. Mat. Vesnik 65 (2013), no. 2, 143-150.
  • [41] Shatanawi, W., Chauhan, S., Postolache, M., Abbas, M., Radanovi´c, S., Common fixed points for contractive mappings in G - metric spaces. J. Adv. Math. Stud. 6 (2013), no. 1, 53-72.
  • [42] Shatanawi, W., Postolache, M., Some fixed point results for a G - weak contraction in G - metric spaces. Abstr. Appl. Anal. (2012), Article ID 815870.
  • [43] Srivastava, R., Agrawal, S., Bhardwaj, R., Vardava, R., Fixed point theorems in complete G - metric spaces. South Asian J. Math. 2 (2013), no. 2, 167-174.
  • [44] Vats, R. K., Kumar, S., Sihang, V., Fixed point theorems in complete G - metric spaces. Fasc. Math. 47 (2011), 127-139.
  • [45] Vetro, C., Vetro, F., Common fixed points of mappings satisfying implicit relations in partial metric spaces. J. Nonlinear Sci. Appl. 6 (2013), 152-161.
  • [46] Zand, M. R. A., Nezhad, A. N., A generalization of partial metric spaces. Appl. Math. 24 (2010), 86-93.

WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES

Year 2015, Volume: 3 Issue: 1, 108 - 117, 15.05.2015

Valeriu Popa , Alina-mihaela Patrıcıu

https://doi.org/10.36753/mathenot.421226
Cited By: 2

Abstract

The purpose of this paper is to prove a general fixed point theorem
in Gp - metric space for mappings satisfying an implicit relation. If Gp - metric
is symmetric, we prove that the fixed point problem is well posed. 

Keywords

Fixed point Gp - metric spaces Well posedness of fixed point problem Implicit relation

References

  • [1] Abbas, M., Nazi, T., Radanovi´c, S., Some periodic point results in generalized metric spaces. Appl. Math. Comput. 217 (2010), 4084-4099.
  • [2] Abdeljawad, T., Karapinar, E., Tas, K., Existence and uniqueness of a common fixed point on partial metric spaces. Appl. Math. Lett. 24 (2011), no. 11, 1900-1904.
  • [3] Akkouchi, M., Popa, V., Well posedness of common fixed point problem for three mappings under strict contractive conditions. Bul. Univ. Petrol - Gaze Ploie¸sti, Ser. Mat. Inform. Fiz. 61 (2009), no. 2, 1-10.
  • [4] Akkouchi, M., Popa, V., Well posedness of a fixed point problem using G - functions. Sci. Stud. Res. Ser. Math. Inform. 20 (2010), 5-12.
  • [5] Akkouchi, M., Popa, V., Well posedness of a fixed point problem for mappings satisfying an implicit relation. Demonstr. Math. 43 (2010), no. 4, 923-929.
  • [6] Akkouchi, M., Popa, V., Well posedness of fixed point problem for hybrid pairs of mappings. Fasc. Math. 46 (2011), 5-16.
  • [7] Altun, I., Sola, F., Simsek, H., Generalized contractions on partial metric spaces. Topology Appl. 157 (2010), no. 18, 2778-2785.
  • [8] Aydi, H., Karapinar, E., Salimi, P., Some fixed point results in Gp-metric spaces. J. Appl. Math. (2012), Article ID 891713.
  • [9] Barakat, M. A., Zidan, A. M., A common fixed point theorem for weak contractive maps in Gp - metric spaces. J. Egyptian Math. Soc. (2014), DOI: 10.1016/j.joems.2014.06.008.
  • [10] Bilgili, N., Karapinar, E., Salimi, P., Fixed point theorems for generalized contractions on Gp - metric spaces. J. Inequalities and Appl. Math.(2013), 2013:39.
  • [11] Chi, R., Karapinar, E., Thanh, T. D., A generalized contraction principle in partial metric spaces. Math. Comput. Modelling 55 (2012), no. 5 - 6, 1673-1681.
  • [12] De Blasi, F. S., Myjak, J., Sur la porosit´e de l’ensemble des contractions sans point fixe. Comptes Rend. Acad. Sci. Paris 308 (1989), 51-54.
  • [13] Dhage, B. C., Generalized metric spaces and mappings with fixed point. Bull. Calcutta Math. Soc. 84 (1992), 329-336.
  • [14] Dhage, B. C., Generalized metric spaces and topological structures I. An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si, Mat. 46 (2000), 3-24.
  • [15] Kadelburg, Z., Nashine, H. K., Radanovic S., Fixed point results under various contractive conditions in partial metric spaces. RACSAM 10 (2013), 241-256.
  • [16] Karapinar, E., Erhan, I. M., Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett. 24 (2011), no. 11, 1900-1904.
  • [17] Kaushal, D. S., Pogey, S. S., Some results of fixed point theorems on complete G - metric spaces. South Asian J. Math. 2 (2014), no. 4, 318-324.
  • [18] Lahiri, B. K., Das, P., Well-posedness and porosity of certain classes of operators. Demonstr. Math. 38 (2005), 170-176.
  • [19] Matthews, S., Partial metric topology and applications. Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728 (1994), 183-197.
  • [20] Mohanta, S., K., Some fixed point theorems in G - metric spaces. An. S¸t. Univ. Ovidius Constant¸a, Ser. Mat. 20 (2012), no. 1, 285-306.
  • [21] Mustafa, Z., Khandagji, M., Shatanawi, W., Fixed point results on complete G - metric spaces. St. Sci. Math. Hungarica 48 (2011), no. 3, 304-319.
  • [22] Mustafa, Z., Obiedat, H., A fixed point theorem of Reich in G - metric spaces. Cubo Math. J. 12 (2010), no. 1, 83-93.
  • [23] Mustafa, Z., Obiedat, H., Awawdeh, F. Some fixed point theorem for mapping on complete G - metric spaces. Fixed Point Theory Appl. (2008), Article ID 189870.
  • [24] Mustafa, Z., Shatanawi, W., Bataineh, M., Existence of fixed point results in G - metric spaces. Intern. J. Math. Math. Sci. (2009), Article ID 283028.
  • [25] Mustafa, Z., Sims, B., Some remarks concerning D - metric spaces. Conf. Fixed Point Theory Appl., Yokohama (2004), 184-198.
  • [26] Mustafa, Z., Sims, B., A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 7 (2006), no. 2, 289-297.
  • [27] Mustafa, Z., Sims, B., Fixed point theorems for contractive mappings in complete G - metric spaces. Fixed Point Theory Appl. (2009), Article ID 917175.
  • [28] Parvaneh, V., Roshan, J. R., Kadelburg, Z., On generalized weakly GP-contractive mappings in ordered GP-metric spaces, Gulf J. Math. 1 (2013), 78-97.
  • [29] Popa, V., Fixed point theorems for implicit contractive mappings. Stud. Cercet. S¸tiint¸., Ser. Mat., Univ. Bac˘au 7 (1997), 129-133.
  • [30] Popa, V., Some fixed point theorems for compatible mappings satisfying an implicit relation. Demonstr. Math. 32 (1999), 157-163.
  • [31] Popa, V., Well posedness of fixed point problem in orbitally complete metric spaces. Stud. Cercet. S¸tiint¸., Ser. Mat., Univ. Bac˘au 16, Suppl. (2006), 209-214.
  • [32] Popa, V., Well posedness of fixed point problem in compact metric spaces. Bul. Univ. Petrol - Gaze Ploie¸sti, Ser. Mat. Inform. Fiz. 60 (2008), no. 1, 1-4.
  • [33] Popa, V., A general fixed point theorem for several mappings in G - metric spaces. Sci. Stud. Res., Ser. Math. Inform. 21 (2011), no. 1, 205-214.
  • [34] 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.
  • [35] 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.
  • [36] Popa, V., Patriciu, A.-M., A general fixed point theorem for pair of weakly compatible mappings in G - metric spaces. J. Nonlinear Sci. Appl. 5 (2012), 151-160.
  • [37] Popa, V., Patriciu, A.-M., Fixed point theorems for mappings satisfying an implicit relation in complete G - metric spaces. Bul. Inst. Politehn. Ia¸si, Ser. Mat. Mec. Teor. Fiz. 59 (63) (2013), 97-123.
  • [38] Reich, S., Zaslavski, A. J., Well posedness of fixed point problem. Far East J. Math. Special Volume, Part III (2001), 393-401.
  • [39] Shatanawi, W., Fixed point theory for contractive mappings satisfying ϕ - maps in G - metric spaces. Fixed Point Theory Appl. (2010), Article ID 181650.
  • [40] Shatanawi, W., Common fixed point results for two self - maps in G - metric spaces. Mat. Vesnik 65 (2013), no. 2, 143-150.
  • [41] Shatanawi, W., Chauhan, S., Postolache, M., Abbas, M., Radanovi´c, S., Common fixed points for contractive mappings in G - metric spaces. J. Adv. Math. Stud. 6 (2013), no. 1, 53-72.
  • [42] Shatanawi, W., Postolache, M., Some fixed point results for a G - weak contraction in G - metric spaces. Abstr. Appl. Anal. (2012), Article ID 815870.
  • [43] Srivastava, R., Agrawal, S., Bhardwaj, R., Vardava, R., Fixed point theorems in complete G - metric spaces. South Asian J. Math. 2 (2013), no. 2, 167-174.
  • [44] Vats, R. K., Kumar, S., Sihang, V., Fixed point theorems in complete G - metric spaces. Fasc. Math. 47 (2011), 127-139.
  • [45] Vetro, C., Vetro, F., Common fixed points of mappings satisfying implicit relations in partial metric spaces. J. Nonlinear Sci. Appl. 6 (2013), 152-161.
  • [46] Zand, M. R. A., Nezhad, A. N., A generalization of partial metric spaces. Appl. Math. 24 (2010), 86-93.
There are 46 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Valeriu Popa

Alina-mihaela Patrıcıu

Publication Date May 15, 2015
Submission Date October 6, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Popa, V., & Patrıcıu, A.-m. (2015). WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES. Mathematical Sciences and Applications E-Notes, 3(1), 108-117. https://doi.org/10.36753/mathenot.421226
AMA Popa V, Patrıcıu Am. WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES. Math. Sci. Appl. E-Notes. May 2015;3(1):108-117. doi:10.36753/mathenot.421226
Chicago Popa, Valeriu, and Alina-mihaela Patrıcıu. “WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES”. Mathematical Sciences and Applications E-Notes 3, no. 1 (May 2015): 108-17. https://doi.org/10.36753/mathenot.421226.
EndNote Popa V, Patrıcıu A-m (May 1, 2015) WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES. Mathematical Sciences and Applications E-Notes 3 1 108–117.
IEEE V. Popa and A.-m. Patrıcıu, “WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES”, Math. Sci. Appl. E-Notes, vol. 3, no. 1, pp. 108–117, 2015, doi: 10.36753/mathenot.421226.
ISNAD Popa, Valeriu - Patrıcıu, Alina-mihaela. “WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES”. Mathematical Sciences and Applications E-Notes 3/1 (May 2015), 108-117. https://doi.org/10.36753/mathenot.421226.
JAMA Popa V, Patrıcıu A-m. WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES. Math. Sci. Appl. E-Notes. 2015;3:108–117.
MLA Popa, Valeriu and Alina-mihaela Patrıcıu. “WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 1, 2015, pp. 108-17, doi:10.36753/mathenot.421226.
Vancouver Popa V, Patrıcıu A-m. WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES. Math. Sci. Appl. E-Notes. 2015;3(1):108-17.

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