. Dipti, Anil Kumar Dubey, Urmila Mishra

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The purpose of this paper is to establish some fixed point results in the setting of metric-like space by defining an (α; β)-admissible z-contraction mapping imbedded in simulation function. Our results generalize and extend several well known results in the literature of fixed point theory. A suitable example is also established to verify the validity of the results obtained.


z-contraction mapping, fixed point, (α; β)-admissible mapping.

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H. Alsamir, M. S. Noorani, W. Shatanawi, H. Aydi, H. Akhadkulov, H. Qawaqneh and K. Alanazi: Fixed point results in metric-like spaces via σ-simulation functions, European Journal of Pure and Appl. Math. 12 (1) (2019), 88-100.

H. H. Alsulami, E. Karapinar, F. Khojasteh and A. F. Roldan-Lopez-deHierro: A proposal to the study of contractions in quasi-metric spaces. Discrete Dynamics in Nature and Society 269286 (2014), 1-10.

A. Amini-Harandi: Metric like spaces, Partial metric spaces and fixed points. Fixed Point Theory and Appl. 204 (2012).

H. Argoubi, B. Samet and C. Vetro: Nonlinear contractions involving simulation functions in a metric space with a partial order. Jour. Nonlinear Sci. Appl. 8 (6) (2015), 1082-1094.

H. Aydi, A. Felhi: Best proximity points for cyclic Kannan-Chatterjea-Ciric type contractions on metric-like spaces. Jour. of Nonlinear Sciences and Applications 9 (5) (2016), 2458-2466.

H. Aydi, A. Felhi and H. Afshari: New Geraghty type contractions on metric-like spaces. Jour. of Nonlinear Sciences and Applications 10 (2) (2017), 780-788.

H. Aydi, A. Felhi, E. Karapinar and S. Sahmim: A Nadler-type fixed point theorem in dislocated spaces and applications. Miscolc, Math. Notes 19 (1) (2018), 111-124.

H. Aydi, A. Felhi and S. Sahmim: Common fixed points via implicit contractions on b-metric-like spaces. Jour. of Nonlinear Sciences and Appl. 10 (4) (2017), 1524-1537.

H. Aydi, A. Felhi and S. Sahmim: On common fixed points for (α; )- contractions and generalized cyclic contractions in b-metric-like spaces and consequences. Jour. of Nonlinear Sciences and Appl. 9 (5) (2016), 2492-2510.

I. Ayoob, N. Z. Chuan and N. Mlaiki: Hardy-Rogers type contraction in double controlled metric like spaces. Aims Mathematics 8 (6), 1362313636 (2023).

F. M. Azmi and S. Haque: Fixed point theory on triple controlled metric-like spaces with a numerical iteration. Symmetry 15 (7) 1403 (2023).

S. Chandok: Some fixed points theorems for (α; β)-admissible Geraghty type contractive mappings and related results. Mathematical Sciences 9 (3) (2015), 127-135.

S.-H. Cho: Fixed point theorem for (α; β) z-contractions in metric spaces. Int. Jour. of Math. Ana. 13 (4) (2019), 161-174.

A. Dewangan, A. K. Dubey, M. D. Pandey and R. P. Dubey: Fixed points for (α; β)-admissible mapping via simulation functions. Comm. Math. Appl. 12 (4) (2021), 1101-1111.

A. Felhi, H. Aydi and D. Zhang: Fixed points for α-admissible contractive mappings via simulation functions Jour. Non. Sci. Appl. 9 (10) (2016), 5544-5560.

F. Khojasteh, S. Shukla and S. Radenovic: A new approach to the study of fixed point theory for simulation functions. Filomat 29 (6) (2015), 1189-1194.

I. Masmali and S. Omran: Chatterjea and Ciric-type fixed-point theorems using (α−)-contraction on C∗-algebra-valued metric space. Mathematics 10 (9) 1615 (2022).

G. Nallaselli, A. J. Gnanaprakasam, G. Mani and O. Ege: Solving integral equations via admissible contraction mappings. Filomat, 36 (14) (2022), 4947-4961.

G. Nallaselli, A. J. Gnanaprakasam, G. Mani, O. Ege, D. Santina and N. Mlaiki A study on fixed point techniques under the α-F-convex contraction with an application. Axioms 12 (2) 139 (2023), 1-18.

A. Padcharoen and P. Sukprasert: On admissible mapping via simulation function. Australian Journal of Math. Anal. and Appl. 18 (1), Art. 14, 10 pages (2021).

S. K. Prakasam, A. J. Gnanaprakasam, O. Ege, G. Mani, S. Haque and N. Mlaiki: Fixed point for an OgF -c O-complete b-metric-like spaces. AIMS Mathematics 8 (1) (2023), 1022-1039.

H. Qawaqneh, M. S. M. Noorani, W. Shatanawi and H. Alsamir: Dommon fixed points for pairs of triangular (α)-admissible mappings. Jour. Non. Sci. Appl., 10 (12) (2017), 6192-6204.

A. F. Roldan-Lopez-de-Hierro, E. Karapinar, C. Roldan-Lopez-de-Hierro and J. Martinez-Moreno: Coincidence point theorems on metric spaces via simulation functions. Jour. Comp. Appl. Math. 275 (2015), 345-355.

B. Samet, C. Vetro and P. Vetro: Fixed point theorem for α − contractive type mappings. Jour. Non. Anal. 75 (4) (2012), 2154-2165.



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