Fixed points of \'{C}iri\'{c} and Caristi-type multivalued contractions
Subject Areas : Fixed point theoryS Yahaya 1 , M. S. Shagari 2 , A. T. Imam 3
1 - Department of Mathematics and Statistics, American University of Nigeria, PMB 2250, Yola, Nigeria
2 - Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
3 - Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
Keywords:
Abstract :
[1] M. Abbas, V. C. Rajic, T. Nazir, S. Radenovic, Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces, Afri. Math. 26 (2015), 17-30.
[2] I. Altun, G. Durmaz, M. Olgun, P-contractive mappings on metric spaces, J. Nonl. Func. Anal. (2018), 2018:43.
[3] M. Arshad, E. Karapinar, J. Ahmad, Some unique fixed point theorems for rational contractions in partially ordered metric spaces, J. Ineq. Appl. (2013), 2013:248.
[4] I. Cabrera, J. Harjani, K. Sadarangani, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Annali. Dell. Univ. Di Ferrara. 59 (2013), 251-258.
[5] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251.
[6] S. Chandok, B. S. Choudhury, N. Metiya, Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions, J. Egypt. Math. Soc. 23 (1) (2015), 95-101.
[7] C. M. Chen, Gh. Heidary Joonaghany, E. Karapinar, F. Khojasteh, On bilateral contractions, Mathematics. 7 (2019), 6:538.
[8] Z. Cheng, The generalization of Ciric and Caristi type fixed point theorem, Wuhan Univ. J. Nat. Sci. 28 (1) (2023), 011-014.
[9] B. S. Choudhury, N. Metiya, C. Bandyopadhyay, P. Maity, Fixed points of multivalued mappings satisfying hybrid rational Pata-type inequalities, The Journal of Analysis. 27 (2019), 813-828.
[10] B. S. Choudhury, N. Metiya, T. Som, C. Bandyopadhyay, Multivalued fixed point results and stability of fixed point sets in metric spaces, Facta Univ. Ser. Math. Info. 30 (2015), 501-512.
[11] L. B. Ciric, A generalization of Banach contraction principle, Proc. Am. Math. Soc. 45 (1974), 267-273.
[12] B. K. Dass, S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math. 6 (12) (1975), 1455-1458.
[13] W. S. Du, E. Karapinar, A note on Caristi-type cyclic maps: Related results and applications, J. Fixed Point Theory Appl. (2013), 2013:344.
[14] D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (2) (1977), 223-230.
[15] E. Karapinar, F. Khojasteh, W. Shatanawi, Revisiting´Ciri´ c type contraction with Caristi approach, Symmetry. 11 (2019), 6:726.
[16] S. B. Nadler, Multi-valued contraction mappings, Paci. J. Math. 30 (2) (1969), 475-488.