## Some Results Regarding \(\varphi\) -maps on G-Cone Metric Spaces with Banach Algebra

Anil Kumar Mishra *

Department of Mathematics, Govt. V.Y.T.P.G. Auto. College, Durg, Chhattisgarh, India.

Padmavati

Department of Mathematics, Govt. V.Y.T.P.G. Auto. College, Durg, Chhattisgarh, India.

*Author to whom correspondence should be addressed.

### Abstract

Aims/ objectives: In our study, we used generalized contraction mapping in G-cone metric space with Banach algebras to establish various fixed point and common fixed point results. Beg [1] defines this space in terms of a few contractive conditions on \(\varphi\) -maps. Our outcomes are a generalization and an extension of several well-known fixed point results.

Keywords: Banach algebras, common fixed point, G-cone metric spaces, generalized Lipschitz conditions

**How to Cite**

*Asian Research Journal of Mathematics*,

*20*(3), 40–50. https://doi.org/10.9734/arjom/2024/v20i3789

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### References

Beg I, Abbas M, Nazır T. Generalized cone metric spaces. The Journal of Nonlinear Science and Applications. 2010;1:21–31.

Banach S. Sur les operations dans ensembles abstraits et leur application aux equations integrals. Fundamenta Mathematicae. 1922;3:133-181.

Dhage B, Pathan AM, Rhoades AM. A general existence principle for fixed point theorems in D-metric spaces. International Journal of Mathematics and Mathematical Sciences. 2000;23:441-448.

Mustafa Z, Sims B. Existence of fixed point results in G-metric spaces. International Journal of Mathematics and Mathematical Sciences. 2009;10.

Huang L, Zhang X. Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 2007;332(2):1468-1476.

Bari C. Di., Vetro P. '-Pairs and common fixed points in cone metric spaces. Rendiconti del Circolo Matematico di Palermo. 2008;57:279–285.

Shatanawi W. Fixed point theory for contractive mappings satisfying '-maps in G-metric spaces. Fixed Point Theory and Appications. 2010;1–9.

Adewale OK, Osawaru EK. G-cone metric spaces over banach algebras and some fixed point results. International Journal of Mathematical Analysis and Optimization: Theory and Applications. 2019;2:546- 557.

Rudin W. Functional analysis. 2nd ed. McGraw-Hill, New York; 1991.

Mishra AK, Padmavati. Some common fixed points theorems using generalize cone metric spaces with Banach Algebra. Bulletin of Mathematics and Statistics Research. 2024;12(1):1-9.

Hao L, Shaoyuan X. Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings. Fixed Point Theory and Applications. 2013:1-10.

Mishra AK, Padmavati. On some fixed point theorem in ordered G-cone metric spaces over Banach Algebra. International Journal of Mathematics And its Applications. 2022;10(4):29-38.

Ahmed A, Salunke JN. Fixed point theorem of expanding mapping without continuity in cone metric space over Banach Algebra. In International Conference on Recent Trends in Engineering and Science. 2017;20:19-22.

Mishra AK, Padmavati, Rathour L, Mishra VN. Some fixed point theorem using generalized cone metric spaces with Banach Algebra. High Technology Letters. 2023;29(1): 153-162.

Mustafa Z, Sims B. Fixed point theorems for contractive mappings in complete G-metric spaces applications. Fixed Point Theory and Applications. 2009;1-10.

Singh N, Jain R. Common fixed point theorems in generalized cone metric. European Journal of Business and Management. 2017;3(4):184-190.

Öztürk MA, Basarir M. On some common fixed point theorems with '-maps on G-cone metric spaces. Bull. Math. Anal. Appl. 2011;3(1):121-133.

Rezapour S, Hamlbarani R. Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings". Journal of Mathematical Analysis and Applications. 2008;345(2):719-724.