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PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings

Year 2024, Volume: 73 Issue: 1, 104 - 121, 16.03.2024
https://doi.org/10.31801/cfsuasmas.1127143

Abstract

In this paper, we introduce the notion of generalized weakly contractive type multi-valued mapping with respect to a single-valued mapping and prove the existence of PPF dependent coincidence points in Banach spaces. Further, we introduce the notion of generalized weakly contractive type multivalued mappings for a pair of multi-valued mappings and prove the existence of PPF dependent common fixed points in Banach spaces. We draw some corollaries and provide nontrivial examples to illustrate our results.

References

  • Alber,Ya. I., Guerre-Delabriere S., Principles of weakly contractive maps in Hilbert spaces New results in operator theory, Adv. Appl., Birkhauser Verlag, 98(1997), 7-22.
  • Babu, G.V.R., Satyanarayana, G., Vinod Kumar, M., Properties of Razumikhin class of functions and PPF dependent fixed points of Weakly contractive type mappings, Bull. Int. Math. Virtual Institute, 9 (2019), 65-72. DOI:10.7251/BIMVI1901065B
  • Babu, G.V.R., Vinod Kumar, M., PPF dependent fixed points of generalized Suzuki type contractions via simulation functions, Advances in the Theory of Nonlinear Anal. and Its Appl., 3 (2019), 121-140. https://doi.org/10.31197/atnaa.588945
  • Babu, G.V.R., Vinod Kumar, M., PPF dependent fixed points of generalized contractions via CG−simulation functions, Communications in Nonlinear Anal., 7 (2019), 1-16.
  • Babu, G.V.R., Vinod Kumar, M., PPF dependent fixed points of generalized weakly contraction maps via CG−simulation functions, Maltepe J. Math., 1 (2019), 66-88.
  • Bae, J. S., Fixed point theorems for weakly contractive multivalued maps, J. Math. Anal. Appl., 284 (2003), 690-697. https://doi.org/10.1016/S0022-247X(03)00387-1
  • Bapurao C. Dhage, On some common fixed point theorems with PPF dependence in Banach space, J. Nonlinear Sci. Appl., 5 (2012), 220-232. https://dx.doi.org/10.22436/jnsa.005.03.06
  • Bernfeld, S. R., Lakshmikantham, V., Reddy, Y. M., Fixed point theorems of operators with PPF dependence in Banach spaces, Appl. Anal., 6 (1977), 271-280.
  • Bose, R. K., Roychowdhury, M. K., Fixed point theorems for generalized weakly contractive mappings, Surveys in Math. Appl., 4 (2009), 215-238.
  • Bose, R. K., Roychowdhury, M. K., Fixed point theorems for multi-valued mapping and fuzzy mappings, Int. J. Pure and App. Math., 61 (2010), 53-72.
  • Chatterjea, S. K., Fixed point theorems, C.R.Acad. Bulgare Sci., 25(1972), 727-730.
  • Choudhury, B. S., Unique fixed point theorems for weackly C-Contractive mappings, Khatmandu University J. Sci. Tech., 1 (2009), 6-12. https://doi.org/10.3126/kuset.v5i1.2842
  • Dirci, Z., McRae, F. A., Vasundharadevi, J., Fixed point theorems in partially ordered metric spaces for operators with PPF dependence, Nonlinear Anal., 67 (2007), 641-647. DOI:10.1016/j.na.2006.06.022
  • Farajzadeh, A., Kaewcharoen, A., Plubtieng, S., PPF dependent fixed point theorems for multivalued mappings in Banach spaces, Bull. Iranian Math.Soc., 42 (2016), 1583-1595.
  • Hussain, N., Khaleghizadeh, S., Salimi, P., Akbar, F., New Fixed Point Results with PPF dependence in Banach Spaces Endowed with a Graph, Abstr. Appl. Anal., 2013, Article ID 827205. https://doi.org/10.1155/2013/827205
  • Kaneko, H., Generalized contractive multi-valued mappings and their fixed points, Math. Japon., 33(1988), 57-64.
  • Kannan, R., Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
  • Marwan Amin Kutbi, Wutiphol Sintunavarat, On sufficient coniditons for the existence of Past-Present-Future dependent fixed point in Razumikhin class and application, Abstr. Appl. Anal., 2014, Article ID 342684. http://dx.doi.org/10.1155/2014/342687
  • Mizoguchi, N., Takahashi, W., Fixed point theorems for multi-valued mappings on complete metric spaces, J. Math. Anal. Appl., 141 (1989), 177-188.
  • Nadler, S.B., Multivalued contraction mappings, Pacific J. Math., 30 (1969), 475-488.
  • Rhoades, B. E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257-290.
  • Rhoades, B. E., Some theorems on weakly contractive mappings, Nonlinear Anal., 47 (2001), 2683-2693. https://doi.org/10.1016/S0362-546X(01)00388-1
Year 2024, Volume: 73 Issue: 1, 104 - 121, 16.03.2024
https://doi.org/10.31801/cfsuasmas.1127143

Abstract

References

  • Alber,Ya. I., Guerre-Delabriere S., Principles of weakly contractive maps in Hilbert spaces New results in operator theory, Adv. Appl., Birkhauser Verlag, 98(1997), 7-22.
  • Babu, G.V.R., Satyanarayana, G., Vinod Kumar, M., Properties of Razumikhin class of functions and PPF dependent fixed points of Weakly contractive type mappings, Bull. Int. Math. Virtual Institute, 9 (2019), 65-72. DOI:10.7251/BIMVI1901065B
  • Babu, G.V.R., Vinod Kumar, M., PPF dependent fixed points of generalized Suzuki type contractions via simulation functions, Advances in the Theory of Nonlinear Anal. and Its Appl., 3 (2019), 121-140. https://doi.org/10.31197/atnaa.588945
  • Babu, G.V.R., Vinod Kumar, M., PPF dependent fixed points of generalized contractions via CG−simulation functions, Communications in Nonlinear Anal., 7 (2019), 1-16.
  • Babu, G.V.R., Vinod Kumar, M., PPF dependent fixed points of generalized weakly contraction maps via CG−simulation functions, Maltepe J. Math., 1 (2019), 66-88.
  • Bae, J. S., Fixed point theorems for weakly contractive multivalued maps, J. Math. Anal. Appl., 284 (2003), 690-697. https://doi.org/10.1016/S0022-247X(03)00387-1
  • Bapurao C. Dhage, On some common fixed point theorems with PPF dependence in Banach space, J. Nonlinear Sci. Appl., 5 (2012), 220-232. https://dx.doi.org/10.22436/jnsa.005.03.06
  • Bernfeld, S. R., Lakshmikantham, V., Reddy, Y. M., Fixed point theorems of operators with PPF dependence in Banach spaces, Appl. Anal., 6 (1977), 271-280.
  • Bose, R. K., Roychowdhury, M. K., Fixed point theorems for generalized weakly contractive mappings, Surveys in Math. Appl., 4 (2009), 215-238.
  • Bose, R. K., Roychowdhury, M. K., Fixed point theorems for multi-valued mapping and fuzzy mappings, Int. J. Pure and App. Math., 61 (2010), 53-72.
  • Chatterjea, S. K., Fixed point theorems, C.R.Acad. Bulgare Sci., 25(1972), 727-730.
  • Choudhury, B. S., Unique fixed point theorems for weackly C-Contractive mappings, Khatmandu University J. Sci. Tech., 1 (2009), 6-12. https://doi.org/10.3126/kuset.v5i1.2842
  • Dirci, Z., McRae, F. A., Vasundharadevi, J., Fixed point theorems in partially ordered metric spaces for operators with PPF dependence, Nonlinear Anal., 67 (2007), 641-647. DOI:10.1016/j.na.2006.06.022
  • Farajzadeh, A., Kaewcharoen, A., Plubtieng, S., PPF dependent fixed point theorems for multivalued mappings in Banach spaces, Bull. Iranian Math.Soc., 42 (2016), 1583-1595.
  • Hussain, N., Khaleghizadeh, S., Salimi, P., Akbar, F., New Fixed Point Results with PPF dependence in Banach Spaces Endowed with a Graph, Abstr. Appl. Anal., 2013, Article ID 827205. https://doi.org/10.1155/2013/827205
  • Kaneko, H., Generalized contractive multi-valued mappings and their fixed points, Math. Japon., 33(1988), 57-64.
  • Kannan, R., Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
  • Marwan Amin Kutbi, Wutiphol Sintunavarat, On sufficient coniditons for the existence of Past-Present-Future dependent fixed point in Razumikhin class and application, Abstr. Appl. Anal., 2014, Article ID 342684. http://dx.doi.org/10.1155/2014/342687
  • Mizoguchi, N., Takahashi, W., Fixed point theorems for multi-valued mappings on complete metric spaces, J. Math. Anal. Appl., 141 (1989), 177-188.
  • Nadler, S.B., Multivalued contraction mappings, Pacific J. Math., 30 (1969), 475-488.
  • Rhoades, B. E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257-290.
  • Rhoades, B. E., Some theorems on weakly contractive mappings, Nonlinear Anal., 47 (2001), 2683-2693. https://doi.org/10.1016/S0362-546X(01)00388-1
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Gutti V. R. Babu 0000-0002-6272-2645

Madugula Vınod Kumar 0000-0001-6469-4855

Publication Date March 16, 2024
Submission Date June 7, 2022
Acceptance Date May 15, 2023
Published in Issue Year 2024 Volume: 73 Issue: 1

Cite

APA Babu, G. V. R., & Vınod Kumar, M. (2024). PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(1), 104-121. https://doi.org/10.31801/cfsuasmas.1127143
AMA Babu GVR, Vınod Kumar M. PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2024;73(1):104-121. doi:10.31801/cfsuasmas.1127143
Chicago Babu, Gutti V. R., and Madugula Vınod Kumar. “PPF Dependent Common Fixed Points of Generalized Weakly Contractive Type Multi-Valued Mappings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 1 (March 2024): 104-21. https://doi.org/10.31801/cfsuasmas.1127143.
EndNote Babu GVR, Vınod Kumar M (March 1, 2024) PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 1 104–121.
IEEE G. V. R. Babu and M. Vınod Kumar, “PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 1, pp. 104–121, 2024, doi: 10.31801/cfsuasmas.1127143.
ISNAD Babu, Gutti V. R. - Vınod Kumar, Madugula. “PPF Dependent Common Fixed Points of Generalized Weakly Contractive Type Multi-Valued Mappings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/1 (March 2024), 104-121. https://doi.org/10.31801/cfsuasmas.1127143.
JAMA Babu GVR, Vınod Kumar M. PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:104–121.
MLA Babu, Gutti V. R. and Madugula Vınod Kumar. “PPF Dependent Common Fixed Points of Generalized Weakly Contractive Type Multi-Valued Mappings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 1, 2024, pp. 104-21, doi:10.31801/cfsuasmas.1127143.
Vancouver Babu GVR, Vınod Kumar M. PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(1):104-21.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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