Fixed points of multivalued mappings satisfying hybrid rational Pata-type inequalities

Abbas, M., V.Ć. Rajić, T. Nazir, and S. Radenović. 2015. Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces. Afrika Matematika 26: 17–30.

Ahmed, M.A. 2003. Common fixed point theorems for weakly compatible mappings. Rocky Mountain Journal of Mathematics 33: 1189–1203.

Altun, I., and D. Turkoglu. 2008. Some fixed point theorems for weakly compatible multivalued mappings satisfying an implicit relation. Filomat 22: 13–21.

Arshad, M., E. Karapinar, and J. Ahmad. 2013. Some unique fixed point theorems for rational contractions in partially ordered metric spaces. Journal of Inequalities and Applications 2013: 248.

Balasubramanian, S. 2014. A Pata-type fixed point theorem. Mathematical Sciences 8: 65–69.

Cabrera, I., J. Harjani, and K. Sadarangani. 2013. A fixed point theorem for contractions of rational type in partially ordered metric spaces. Annali Dell’Universita’Di Ferrara 59: 251–258.

Chandok, S., and J.K. Kim. 2012. Fixed point theorem in ordered metric spaces for generalized contractions mappings satisfying rational type expressions. Journal of Nonlinear Functional Analysis 17: 301–306.

Chandok, S., B.S. Choudhury, and N. Metiya. 2015. Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions. Journal of the Egyptian Mathematical Society 23 (1): 95–101.

Choudhury, B.S., N. Metiya, and P. Maity. 2013. Coincidence point results of multivalued weak C-contractions on metric spaces with a partial order. Journal of Nonlinear Sciences & Applications 6: 7–17.

Choudhury, B.S., N. Metiya, T. Som, and C. Bandyopadhyay. 2015. Multivalued fixed point results and stability of fixed point sets in metric spaces. Facta Universitatis, Series: Mathematics and Informatics 30: 501–512.

Choudhury, B.S., N. Metiya, and C. Bandyopadhyay. 2015. Fixed points of multivalued $$\alpha$$ α -admissible mappings and stability of fixed point sets in metric spaces. Rendiconti del Circolo Matematico di Palermo 64: 43–55.

Choudhury, B.S., N. Metiya, and S. Kundu. 2018. End point theorems of multivalued operators without continuity satisfying hybrid inequality under two different sets of conditions. Rendiconti del Circolo Matematico di Palermo Series. https://doi.org/10.1007/s12215-018-0344-z .

Dass, B.K., and S. Gupta. 1975. An extension of Banach contraction principle through rational expressions. Indian Journal of Pure and Applied Mathematics 6: 1455–1458.

Harjani, J., B. López, and K. Sadarangani. 2010. A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space. Abstract and Applied Analysis 2010: 190701. https://doi.org/10.1155/2010/190701 .

Jaggi, D.S., and B.K. Das. 1980. An extension of Banach’s fixed point theorem through rational expression. Bulletin of the Calcutta Mathematical Society 72: 261–264.

Kadelburg, Z., and S. Radenović. 2015. A note on Pata-type cyclic contractions. Sarajevo Journal of Mathematics 11 (2): 235–245.

Kadelburg, Z., and S. Radenović. 2016. Fixed point theorems under Pata-type conditions in metric spaces. Journal of the Egyptian Mathematical Society 24: 77–82.

Kannan, R. 1968. Some results on fixed points. Bulletin of the Calcutta Mathematical Society 60: 71–76.

Kannan, R. 1969. Some results of fixed points-II. American Mathematical Monthly 76: 405–408.

Kolagar, S.M., M. Ramezani, and M. Eshaghi. 2016. Pata type fixed point theorems of multivalued operators type fixed point theorems of multivalued operators in ordered metric spaces with applications to hyperbolic differential inclusions. UPB Scientific Bulletin, Series A 78 (4): 21–34.

Kumam, P., F. Rouzkard, Md Imdad, and D. Gopal. 2013. Fixed point theorems on ordered metric spaces through a rational contraction. Abstract and Applied Analysis 2013: 206515. https://doi.org/10.1155/2013/206515 .

Luong, N.V., and N.X. Thuan. 2011. Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces. Fixed Point Theory and Applications 46: 1–10.

Nadler Jr., S.B. 1969. Multivalued contraction mapping. Pacific Journal of Mathematics 30: 475–488.

Pata, V. 2011. A fixed point theorem in metric spaces. Journal of Fixed Point Theory and Applications 10: 299–305.

Reich, S. 1971. Kannan’s fixed point theorem. Bollettino dell’Unione Matematica Italiana 4: 1–11.

Reich, S. 1972. Fixed points of contractive functions. Bollettino dell’Unione Matematica Italiana 5: 26–42.