Some Common Fixed Point on Generalized Cyclic Contraction Mappings with Implicit Relation and Its Applications

Nantaporn Chuensupantharat, Poom Kumam

Abstract


From the concept of cyclic relation, we introduced the generalized cyclic contraction with respect to multi-valued mappings under implicit relation and obtained some common fixed point theorem in complete metric spaces. In addition, some examples and applications are presented to demonstrate our results.

Keywords


Cyclic contraction; Multivalued mapping; Implicit function

Full Text:

PDF

References


B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1) (1977), 257–290.

B.K. Robati, M.B. Pour and C. Ionescu, Common fixed point results for cyclic operators on complete matric spaces, U.P.B. Sci. Bull. 77 (2) (2015), 59–66.

H.K. Nashine, Z. Kadelburg and P. Kumam, Implicit-relation-type cyclic contractive mappings and applications to integral equations, Abstract and Applied Analysis 2012 (2012).

H.K. Nashine, Fixed point and cyclic contraction mappings under implicit relations and applications to integral equation, Sarajevo J. Math. 10 (2014), 257–270.

H.K. Nashine and I. Altun, New fixed point results for maps satisfying implicit relations on ordered metric spaces and application, Applied Mathematics and Computation 240 (2014), 259–272.

I. Altun and H. Simsek, Some fixed point theorems on ordered metric spaces and applications, Fixed Point Theory Appl. 2010, Article ID 621469, 17 p.

K. Neammanee and A. Kaewkhao, Fixed points and best proximity points for multi-valued mapping satisfying cyclical condition, Math. Sci. Appl. 1 (2011), ??–??.

P.S. Kumari and D. Panthi, Cyclic contractions and fixed point theorems on various generating spaces, Fixed Point Theory 2015 (2015), 153, doi 10.1186/s13663-015-0403-5.

S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae 3 (1922), 133–181.

S.B. Nadler, Jr., Multi-valued contraction mappings, Pacific Journal of Mathematics 30 (1969), 475–488.

V. Berinde, Approximation fixed points of implicit almost contractions, Hacettepe Journal of Mathematics and Statistics 41 (2012), 93–102.

V. Berinde and F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory Appl. 2012 (2012), 105.

V. Popa, A general fixed point theorem for implicit cyclic multi-valued contraction mappings, Annales Mathematicae Silesianae 29 (2015), 119–129.

W.A. Kirk, P.S. Srinivasan and P. Veeramani, Fixed point for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4 (1) (2003), 79–89.

W. Shatanawi, A. Bataihah and A. Pitea, Fixed and common fixed point results for cyclic mappings of Ω-distance, J. Nonlinear Sci. Appl. 9 (2016), 727–735.


Refbacks

  • There are currently no refbacks.


eISSN 0975-8607; pISSN 0976-5905