Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions
Year 2024,
Volume: 12 Issue: 1, 12 - 19, 28.01.2024
Gonca Durmaz Güngör
,
İshak Altun
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.
References
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[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).
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[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).
Year 2024,
Volume: 12 Issue: 1, 12 - 19, 28.01.2024
Gonca Durmaz Güngör
,
İshak Altun
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).