Quasi weak – partial cone b – metric space and some fixed point results

**MLA Style: **Eriola Sila, Silvana Liftaj, Kujtim Dule. "Quasi weak – partial cone b – metric space and some fixed point results" International Journal of Mathematics Trends and Technology 67.2 (2021):159-165. **APA Style: **Eriola Sila, Silvana Liftaj, Kujtim Dule(2021). Quasi weak – partial cone b – metric space and some fixed point results. International Journal of Mathematics Trends and Technology, 159-165.

**Abstract**

Let X be a non – empty set. In this paper is given a new space called the quasi weak – partial cone b - metric space X. There are defined right (left) open balls, right (left) closed balls, right topology, left topology, right Cauchy sequences, left Cauchy sequences and right (left) convergent sequences in it. Furthermore, there is proved the existence and uniqueness of a fixed point related to a nonlinear contraction using a comparison function in X. Some results are obtain as corollaries. These results generalize some well - known theorems in quasi weak - partial cone metric space. In addition, as illustrations are given some examples.

**Reference**

[1] Huang L.G., Zhang X., Cone metric spaces and fixed point theorems of contractive mappings, J.Math.Anal. Appl. 332(2007) 1468-1476.

[2] Branga AN, Olaru IM. Cone Metric Spaces over Topological Modules and Fixed Point Theorems for Lipschitz Mappings. Mathematics. 8(5)(2020) 724.

[3] Shatanawi W, D. Mitrović Z, Hussain N, Radenović S., On Generalized Hardy–Rogers Type α- Admissible Mappings in Cone b-Metric Spaces over Banach Algebras. Symmetry.12(1)(2020) 81.

[4] Nazam, M., Arif, A., Mahmood, H., & Park, C., Some results in cone metric spaces with applications in homotopy theory. Open Mathematics, 18(1), (2020) 295-306

[5] Q. Meng, On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems, Chinese Annals of Mathematics, Series B, 40(3)(2019) 429–438,

[6] S.-H. Cho, Fixed Point Theorems in Complete Cone Metric Spaces over Banach Algebras, Journal of Function Spaces, (2018) 9395057

[7] Matthews S. G., Partial metric topology, Annals of the New York Academy of Sciences, Proc. 8th Summer Conference on General Topology and Applications. 728(1994) 183–197,

[8] Heckmann R. Approximation of a metric space by partial metric space, Applied Categorical Structures 7(1999) 71–83.

[9] Beg, I., Pathak, H.K. A Variant of Nadler’s Theorem on Weak Partial Metric Space wit Application to a Homotopy Result. Vietnam J. Math. 46(2018) 693 – 706

[10] Aydi H, Barakat MA, Mitrović ZD, Šešum-Čavić V. A Suzuki-type multivalued contraction on weak partial metric spaces and applications. J Inequal Appl. (1)(2018) 270.

[11] Kanwal T, Hussain A, Kumam P, Savas E. Weak Partial b-Metric Spaces and Nadler’s Theorem. Mathematics. 7(4)(2019) 332.

[12] Durmaz, G., Acar, Ö, & Altun, I.. Some fixed point results on weak partial metric spaces. Filomat, 27(2)(2013) 317-326.

[13] Popa, V., & Patriciu, A. Fixed Point Theorem of Ćirić Type in Weak Partial Metric Spaces. Filomat, 31(11)(2017) 3203-3207.

[14] Zidan, A. M., & Al Rwaily, A. On New Type of F -Contractive Mapping for Quasipartial b -Metric Spaces and Some Results of Fixed-Point Theorem and Application. Journal of Mathematics, (2020).

[15] Barakat M. A., Ahmed M.A., Zidan A.M. Weak – Partial Metric Spaces and Fixed Point Results, International Journal of Advances in Mathematics. 6(2017) 123 – 126

[16] Hussain N., Kadelburg Z., Radenovic S., Al – Solami F., Comparison functions and fixed point results in partial metric spaces. Abstr. Appl. Anal (2012) Article ID 605781

[17] Ciric Lj. B., A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45(1974) 267 - 273.

[18] Hardy G. E., Rogers T. D. A generalization of a fixed point theorem of Reich, Canad. Math.Bull.16(1973) 201 – 206

[19] Bianchini R. M. T. Su un problema di S. Reich aguardante la teoría dei punti fissi, Boll.Un. Mat.Ital.5(1972) 103-108.

[20] Sila E., Aplikime në Gjeometri të disa rezultateve të pikave fike, www.fshn.edu.al: (2015) 6 – 7.

**Keywords : **Cauchy sequence, convergent sequence, comparison function, fixed point, quasi weak – partial b – cone metric space