Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions

Year 2024, , 12 - 19, 28.01.2024

Gonca Durmaz Güngör İshak Altun

https://doi.org/10.36753/mathenot.1300609

Cited By: 1

Abstract

By implying $\alpha $-admissible mapping, this study expands and investigates generalized contraction mappings in quasi-metric spaces, aiming to establish the existence of fixed points. Moreover, we show that the main outcomes of the paper encompass several previously reported results in the literature.

Keywords

Fixed point, Right $K$-Cauchy sequence, Quasi metric space, $\alpha $ admissible

References

• [1] Boyd, D.W., Wong, J. S.W.: On nonlinear contractions. Proceedings of the American Mathematical Society. 20, 458-464 (1969).
• [2] Ciric, Lj. B.: A generalization of Banach’s contraction principle. Proceedings of the American Mathematical Society. 45, 267-273 (1974).
• [3] Hardy, G. E., Rogers, T. D.: A generalization of a fixed point theorem of Reich. Canadian Mathematical Bulletin. 16, 2021-206 (1973).
• [4] Matkowski, J.: Fixed point theorems for mappings with a contractive iterate at a point. Proceedings of the American Mathematical Society. 62(2), 344-348 (1977).
• [5] Zamfirescu, T.: Fix point theorems in metric spaces, Archiv der Mathematik. 23, 292-298 (1972).
• [6] Alegre, C., Mar´ın, J., Romaguera, S.: A fixed point theorem for generalized contractions involving w-distances on complete quasi metric spaces. Fixed Point Theory and Applications. 2014, 1-8 (2014).
• [7] Gaba, Y. U.: Startpoints and (-)-contractions in quasi-pseudometric spaces, Journal of Mathematics. 2014, 8 pages (2014).
• [8] Latif, A., Al-Mezel, S. A.: Fixed point results in quasimetric space. Fixed Point Theory and Applications. 2011, 1-8 (2011).
• [9] Marın, J., Romaguera, S., Tirado, P.: Weakly contractive multivalued maps and w-distances on complete quasimetric spaces. Fixed Point Theory and Applications. 2011, 1-9 (2011).
• [10] Marın, J., Romaguera, S., Tirado, P.: Generalized contractive set-valued maps on complete preordered quasi-metric spaces. Journal of Function Spaces and Applications. 2013, 6 pages (2013).
• [11] Reilly, I. L., Subrahmanyam, P. V., Vamanamurthy, M. K.: Cauchy sequences in quasi- pseudo-metric spaces. Monatshefte für Mathematik. 93, 127-140 (1982).
• [12] Romaguera, S.: Left K-completeness in quasi-metric spaces. Mathematische Nachrichten. 157, 15-23 (1992).
• [13] Şimşek, H., Altun, İ.: Two type quasi-contractions on quasi metric spaces and some fixed point results. The Journal of Nonlinear Sciences and Applications. 10, 3777-3783 (2017).
• [14] Şimsek, H., Yalcin, M. T.: Generalized Z-contraction on quasi metric spaces and a fixed point result. The Journal of Nonlinear Sciences and Applications. 10, 3397-3403 (2017).
• [15] Altun, İ., Mınak, G., Olgun, M.: Classification of completeness of quasi metric space and some new fixed point results. Nonlinear functional analysis and applications. 371-384 (2017).
• [16] Samet, B., Vetro, C., Vetro, P.: Fixed point theorems for  􀀀 -contractive type mappings. Nonlinear Analysis. 75, 2154-2165 (2012).
• [17] Ali, M. U., Kamran, T., Shahzad, N.: Best proximity point for  􀀀 -proximal contractive multimaps. Abstract and Applied Analysis. 2014, 6 pages (2014).
• [18] Altun, İ., Al Arifi, N., Jleli, M., Lashin, A., Samet, B.: A new concept of (; Fd)-contraction on quasi metric space.
• The Journal of Nonlinear Sciences and Applications. 9, 3354-3361 (2016).
• [19] Durmaz, G., Mınak, G., Altun, ˙I.: Fixed point results for  􀀀 -contractive mappings including almost contractions and applications. Abstract and Applied Analysis. 2014, 10 pages (2014).
• [20] Hussain, N., Karapınar, E., Salimi, P., Akbar, F.: -admissible mappings and related fixed point theorems. Journal of Inequalities and Applications. 2013, 11 pages (2013).
• [21] Hussain, N., Vetro, C., Vetro, F.: Fixed point results for -implicit contractions with application to integral equations. Nonlinear Analysis: Modelling and Control. 21(3), 362-378 (2016).
• [22] Karapınar, E., Samet, B.: Generalized Alpha-Psi -contractive type mappings and related fixed point theorems with applications. Abstract and Applied Analysis. 2012, 17 pages (2012).
• [23] Kumam, P., Vetro, C., Vetro, F.: Fixed points for weak  􀀀 -contractions in partial metric spaces. Abstract and Applied Analysis. 2013, 9 pages (2013).
• [24] Jleli, M., Samet, B.: A new generalization of the Banach contraction principle. Journal of Inequalities and Applications. 2014, 1-8 (2014).
• [25] Altun, İ., Hançer, H. A., Mınak, G.: On a general class of weakly Picard operators. Miskolc Mathematical Notes. 16(1), 25-32 (2015).
• [26] Jleli, M., Karapinar, E., Samet, B.: Further generalizations of the Banach contraction principle. Journal of Inequalities and Applications. 2014(1), 1-9 (2014).