Some results on MKKCR-type coupling on complete metric space

Dakjum  Eshi; Bipan Hazarika; Nipen Saikia

doi:10.5269/bspm.69351

Dakjum Eshi Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh
Bipan Hazarika Rajiv Gandhi University
Nipen Saikia Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh

Abstract

The terms MKKCR type coupling, MKKR type coupling, and MKCR type coupling are defined in this study by fusing the concepts of coupled fixed points, cyclic contractions, and Meir-Keeler mappings. In the context of entire metric space, several results of strongly coupled fixed points are produced for these contraction mappings. We provide an illustration to back up our main finding. It has also been argued how our main finding can be applied to the question of whether a class of nonlinear integral equations exists. Our findings generalize a number of previously published findings on coupled fixed points, particularly findings related to Chatterjea and Kannan type contractions.

Downloads

Download data is not yet available.

Author Biographies

Dakjum Eshi, Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh

Department of Mathematics, Assistant Proefessor

Bipan Hazarika, Rajiv Gandhi University

Mathematics

Professor

Nipen Saikia , Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh

Department of Mathematics, Associate Professor

References

Abdeljawad, T., Karapinar, E. and H. Aydi, H., Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces. Math. Probl. Eng. 2012, Article ID 327273, 20 pages, (2012). https://doi.org/10.1155/2012/327273

Aydi, H., I¸sık, H., Barakat, M.A. and Felhi, A. On symmetric Meir-Keeler contraction type couplings. Filomat 36(9), (2022).

Aydi, H., I¸sık, H., Barakat, M.A. and Felhi, A. Fixed point results for couplings on abstract metric spaces and application. J. Inequal. Spec. Funct. 9(2), 57-67, (2018).

Aydi, H., Karapinar, E., New Meir-Keeler Type Tripled Fixed-Point Theorems on Ordered Partial Metric Spaces. Math. Probl. Eng. 2012, Article ID 409872, 17 pages, (2012). https://doi.org/10.1155/2012/409872

Aydi, H., Karapinar, E., A Meir-Keeler common type fixed point theorem on partial metric spaces. Fixed Point Theory Appl. 2012, Article number 26, (2012). https://doi.org/10.1186/1687-1812-2012-26

Bhaskar, T. G. and Lakshmikantham, V., Fixed point theorems in partially ordered metric spaces and applications. Nonlin. Anal. 65, 1379-1393, (2006).

Tripathy, B.C., Paul, S. and Das,N.R., A fixed point theorem in a generalized fuzzy metric space. Bol. Soc. Parana. Mat. 32(2), 221-227, (2014).

Tripathy, B.C., Paul, S. and Das,N.R., Fixed point and periodic pint theorems in fuzzy metric space. Songklanakarin Jour. Sci. Technol. 37(1), 89-92, (2015).

Tripathy, B.C., Paul, S. and Das,N.R., Some Fixed Point Theorems in Generalized M-Fuzzy Metric Space. Bol. Soc. Parana. Mat. 41, 1-7, (2023).

Chatterjea, S.K., Fixed point theorems. C.R. Acad. Bulgare Sci. 25(6), 727-730, (1972).

Chen, C. and Kuo, C., Best proximity point theorems of cyclic Meir-Keeler-Kannan-Chatterjea contractions. Results Nonlinear Anal. 2, 83-91, (2019).

Choudhury, B.S. and Maity, P., Cyclic Coupled Fixed Point Result Using Kannan Type Contractions. J. Oper. 2014(4), 1-5, (2014).

Choudhury, B.S., Maity, P. and Konar, P., Fixed point results for couplings on metric space. U.P.B. Sci. Bull. Series A 79, 1-12, (2017).

Eshi, D., Hazarika, B. and Saikia, N., Some results on cyclic Meir-Keeler Kannan-Chatterjea-Reich type contraction mappings on complete metric space. Bol. Soc. Parana. Mat. (To Appear).

Guo, D. and Lakshmikantham, V., Coupled fixed points for non linear operators with application. Nonlinear Anal. 11(5), 623-632, (1987).

Hristov, M., Ilchev, A. and Zlatanov, B., Coupled fixed points for Chatterjea type maps with the mixed monotone property in partially ordered metric spaces. AIP Conf. Proc. 2172, 060003, (2019). https://doi.org/10.1063/1.5133531

Kannan, R., Some results on fixed points. Bull. Calc. Math. Soc. 60(1), 71-77, (1968).

Kirk, W.A., Srinivasan, P.S. and Veeramani, P., Fixed points for mapping satisfying cyclical contractive conditions. Fixed Point Theory Appl. 4(1), 79-89, (2003).

Meir, A. and Keeler, E.B., A theorem on contraction mappings. J. Math. Anal. Appl. 28, 326-329, (1969).

Rashid, T. and Khan, Q.H., Strong coupled fixed point for (ϕ, ψ)− contraction type coupling in metric space. Int. J. Adv. Sci. Technol. 7(1), (2018).

Reich, S., Some remarks concerning contraction mappings. Canad. Math. Bull. 14 (1), 121-124, (1971).

Rhoades, B.E., A comparison of various definations of contractive mappings. Trans. Amer. Math. Soc. 26, 257-290, (1977).

Das, A., Rabbani, M., Mohiuddine, S. A. and Deuri, B. C., Iterative algorithm and theoretical treatment of existence of solution for (k, z)-Riemann-Liouville fractional integral equations. J. Pseudo-Differ. Oper. Appl. 13, article number 39, (2022).

Mohiuddine, S. A., Das, A. and Alotaibi, A., Existence of solutions for infinite system of nonlinear q-fractional boundary value problem in Banach spaces, Filomat 37(30), 10171-10180, (2023).

Mustafa, Z. and Sims, B., A new approach to generalized metric spaces. Jour. Nonlinear Conv. Anal. 7(2), 289-297, (2006).

Sintunavarat, W., Kumam, P. and Cho, Y.J., Coupled fixed point theorems for nonlinear contractions without mixed monotone property. Fixed Point Theory Appl. 2012, article number 170, (2012). https://doi.org/10.1186/1687-1812-2012-170