TY - JOUR T1 - PPF Dependent common fixed points of generalized weakly contractive type multi-valued mappings AU - Vınod Kumar, Madugula AU - Babu, Gutti V. R. PY - 2024 DA - March Y2 - 2023 DO - 10.31801/cfsuasmas.1127143 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 104 EP - 121 VL - 73 IS - 1 LA - en AB - 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. KW - Multi-valued mapping KW - Razumikhin class KW - PPF dependent coincidence point KW - PPF dependent fixed point KW - PPF dependent common fixed point CR - 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. CR - 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 CR - 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 CR - 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. CR - 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. CR - 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 CR - 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 CR - 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. CR - Bose, R. K., Roychowdhury, M. K., Fixed point theorems for generalized weakly contractive mappings, Surveys in Math. Appl., 4 (2009), 215-238. CR - 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. CR - Chatterjea, S. K., Fixed point theorems, C.R.Acad. Bulgare Sci., 25(1972), 727-730. CR - 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 CR - 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 CR - 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. CR - 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 CR - Kaneko, H., Generalized contractive multi-valued mappings and their fixed points, Math. Japon., 33(1988), 57-64. CR - Kannan, R., Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76. CR - 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 CR - Mizoguchi, N., Takahashi, W., Fixed point theorems for multi-valued mappings on complete metric spaces, J. Math. Anal. Appl., 141 (1989), 177-188. CR - Nadler, S.B., Multivalued contraction mappings, Pacific J. Math., 30 (1969), 475-488. CR - Rhoades, B. E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257-290. CR - 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 UR - https://doi.org/10.31801/cfsuasmas.1127143 L1 - https://dergipark.org.tr/en/download/article-file/2471403 ER -