Fixed point results for orthogonal G-F- Contraction mappings on O-complete G- metric spaces

  • G Sudhaamsh Mohan Reddy ICFAI Foundation for Higher Education

Abstract

In this manuscript, we introduce the notion of an orthogonal G-F- contraction mapping and establish fixed points results for such contraction mappings in orthogonally G- metric spaces.

Downloads

Download data is not yet available.

Author Biography

G Sudhaamsh Mohan Reddy, ICFAI Foundation for Higher Education

Assistant Professor

Faculty of Science and Technology

References

Banach, S., Sur les operationsdans les ensembles abstraitsetleurs applicationsaux equations integrales, Fund.Math.3, 133–181 (1992).

Berinde, V., Iterative approximation of fixed points, Springer, Berlin, Heidelberg(2007).

Boyd, D.W., Wong, J.S.W., On nonlinear contractions, Proc. Am. Math. Soc.20, 458–464(1969).

Cho, Y.J., Survey on metric fixed point theory and applications. In M. Ruzhanskyet al.(eds.) Advances in Real and Complex Analysis with Applications,Trends in Math, pp. 183-241, Springer Singapore,(2017).

Ciric, L.J.B., A generalization of Banach’s contraction principle, Proc. Am.Math. Soc,45,267-273(1974).

Du, W.S., Some new results and generalizations in metric fixed point theory, Nonlinear Anal,73, 1439-1446(2010).

Gordji, M.E., Rameani, M., De La Sen, M., Cho, Y.J. On orthogonal sets andBanach fixed point theorem, Fixed Point Theory 18,569-578(2017).

G S M Reddy, A Common Fixed Point theorem on complete G-metric spaces, International Journal of Pure and Applied Mathematics, 118, 195-202, (2018).

G S M Reddy, Fixed point theorems of contractions of G-metric Spaces and property’P’in G-Metric spaces, Global Journal of Pure and Applied Mathematics, 14, 885-896, (2018).

G S M Reddy, Fixed Point Theorems for (ε, λ)-Uniformly Locally Generalized Contractions, Global Journal of Pure and Applied Mathematics, 14, 1177-1183, (2018).

G S M Reddy, New proof for generalization of contraction principle on G-Metric spaces, Jour of Adv Research in Dynamical and Control Systems, Vol. 11,Special Issue-08, 2708-2713(2019).

G S M Reddy, V Srinivas Chary.,Srinivasa Chary D, Stojan Radenovic and Slobodanka Mitrovic, Coupled fixed point theorems of JS-G-contraction on G-metric spaces, Boletim da Sociedade Paranaense de Matematica, 41, 1–10(2023) .

G S M Reddy, Fixed point theorems of Rus -Reich -Ciri ´c type contraction and Hardy- Rogers type contraction on G-metric spaces, International Journal of Advanced Science and Technology Vol.29, No.2, 2782-2787(2020).

G S M Reddy, Generalized Ciri´c Type Contraction in G - metric spaces, International Journal of Grid and Distributed Computing Vol.13, No.1, 302-308(2020).

G S M Reddy, Srinivas Chary V.,Srinivasa Chary D., Hseyin Isik and Aydi Hassen, Some fixed point theorems for modified JS-G-contractions and an application to integral equation, Journal of Applied Mathematics and Informatics. 38, No. 5-6, 507-518(2020).

Hardy, G.E., Rogers, T.D., A generalization of a fixed point theorem of Reich, Can. Math.Bull., 16,201-206(1973)

KanokwanSawangsup, WutipholSintunavarat and Yeol Je Cho., Fixed point Theorems for orthogonal F-contraction mappings on O-completemetric spaces, J. Fixed Point Theory Appl.(2020)22:10.

Matkowski, J., Fixed point theorems for mappings with a contractive iterateat a point, Proc. Am. Math. Soc., 62,344-348(1977).

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7(2),289-297(2006).

Nieto, J.J., Rodr´ıguez-L´opez, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22,223-239(2005).

Ran, A.C.M., Reuring, M.C.B., A fixed point theorem in partially ordered sets and some appllications to matrix equations, Proc. Am. Math. Soc. 132, 1435-1443(2004).

Reich, S., Some remarks concerning contraction mappings, Can. Math. Bull. 14,121-12(1971)

Reich, S., Kannan’s fixed point theorem, Boll. Della Unione Matematica Italiana 4(4),11(1971).

Rhoades, B.E., Some theorems on weakly contractive maps, Nonlinear Anal.47, 2683-2693(2001).

Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proc. Am. Math. Soc. 136, 1861-1869(2008).

Srinivas Chary V., G S M Reddy, Srinivasa Chary D, Hseyin Isik and Aydi Hassen,, Some fixed point theorems on α − β−G-complete G-metric spaces, Carpathian Mathematical Publications. 13, 1, 58–67(2021).

Srinivas Chary V, G S M Reddy, Srinivasa Chary D, Stojan Radenovic., Existence of fixed points in G-metric spaces, Boletim da Sociedade Paranaense de Matematica, 41, 1–18(2023).

Wardowski, D., Fixed points of a new type of contractive mappings in completemetric spaces, Fixed Point Theory Appl. 2012,94(2012).

Yan, F., Su, Y., Feng, Q., A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differenctial equations, Fixed Point Theory Appl.2012,152(2012).

Published
2025-09-01
Section
Research Articles