In this paper, we establish a new fixed point result for Hardy-Rogers type contractions in double controlled metric-like spaces. Our result generalizes many important theorems in the literature. We will provide an example to illustrate our results.
Citation: Irshad Ayoob, Ng Zhen Chuan, Nabil Mlaiki. Hardy-Rogers type contraction in double controlled metric-like spaces[J]. AIMS Mathematics, 2023, 8(6): 13623-13636. doi: 10.3934/math.2023691
In this paper, we establish a new fixed point result for Hardy-Rogers type contractions in double controlled metric-like spaces. Our result generalizes many important theorems in the literature. We will provide an example to illustrate our results.
[1] | A. Al-Rawashdeh, H. Aydi, A. Felhi, S. Sehmim, W. Shatanawi, On common fixed points for $\alpha$-$F$-contractions and applications, J. Nonlinear Sci. Appl., 9 (2016), 3445–3458. http://dx.doi.org/10.22436/jnsa.009.05.128 doi: 10.22436/jnsa.009.05.128 |
[2] | W. Shatanawi, Z. Mustafa, N. Tahat, Some coincidence point theorems for nonlinear contraction in ordered metric spaces, Fixed Point Theory Appl., 2011 (2011), 68. http://dx.doi.org/10.1186/1687-1812-2011-68 doi: 10.1186/1687-1812-2011-68 |
[3] | W. Shatanawi, Some fixed point results for a generalized $\Psi$-weak contraction mappings in orbitally metric spaces, Chaos Soliton. Fract., 45 (2012), 520–526. http://dx.doi.org/10.1016/j.chaos.2012.01.015 doi: 10.1016/j.chaos.2012.01.015 |
[4] | S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, 1 (1993), 5–11. |
[5] | T. Kamran, , M. Samreen, Q. Ain, A generalization of b-metric space and some fixed point theorems, Mathematics, 5 (2017), 19. http://dx.doi.org/10.3390/math5020019 doi: 10.3390/math5020019 |
[6] | W. Shatanawi, T. Shatnawi, New fixed point results in controlled metric type spaces based on new contractive conditions, AIMS Mathematics, 8 (2023), 9314–9330. http://dx.doi.org/10.3934/math.2023468 doi: 10.3934/math.2023468 |
[7] | A. Rezazgui, A. Tallafha, W. Shatanawi, Common fixed point results via $A\nu$-$\alpha$-contractions with a pair and two pairs of self-mappings in the frame of an extended quasi b-metric space, AIMS Mathematics, 8 (2023), 7225–7241. http://dx.doi.org/10.3934/math.2023363 doi: 10.3934/math.2023363 |
[8] | M. Joshi, A. Tomar, T. Abdeljawad, On fixed points, their geometry and application to satellite web coupling problem in $S$-metric spaces, AIMS Mathematics, 8 (2023), 4407–4441. http://dx.doi.org/10.3934/math.2023220 doi: 10.3934/math.2023220 |
[9] | N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics, 6 (2018), 194. http://dx.doi.org/10.3390/math6100194 doi: 10.3390/math6100194 |
[10] | D. Lattef, Kannan fixed point theorem in C-metric spaces, J. Math. Anal., 10 (2019), 30–40. |
[11] | J. Ahmad, A. Al-Mazrooei, H. Aydi, M. De la Sen, On fixed point results in controlled metric spaces, J. Funct. Space., 2020 (2020), 2108167. http://dx.doi.org/10.1155/2020/2108167 doi: 10.1155/2020/2108167 |
[12] | T. Abdeljawad, N. Mlaiki, H. Aydi, N. Souayah, Double controlled metric type spaces and some fixed point results, Mathematics, 6 (2018), 320. http://dx.doi.org/10.3390/math6120320 doi: 10.3390/math6120320 |
[13] | N. Mlaiki, Double controlled metric-like spaces, J. Inequal. Appl., 2020 (2020), 189. http://dx.doi.org/10.1186/s13660-020-02456-z doi: 10.1186/s13660-020-02456-z |
[14] | A. Tas, On double controlled metric-like spaces and related fixed point theorems, Advances in the Theory of Nonlinear Analysis and its Application, 5 (2021), 167–172. http://dx.doi.org/10.31197/atnaa.869586 doi: 10.31197/atnaa.869586 |
[15] | G. Hardy, T. Rogers, A generalization of a fixed point theorem of Reich, Can. Math. Bull., 16 (1973), 201–206. http://dx.doi.org/10.4153/CMB-1973-036-0 doi: 10.4153/CMB-1973-036-0 |