The construction of contraction conditions plays an important role in science for formulating new findings in fixed point theories of mappings under a set of specific conditions. The aim of this work is to take advantage of the idea of extended $ b $-metric spaces in the sense introduced by Kamran et al. [A generalization of $ b $-metric space and some fixed point theorems, Mathematics, 5 (2017), 1–7] to construct new contraction conditions to obtain new results related to fixed points. Our results enrich and extend some known results from $ b $-metric spaces to extended b-metric spaces. We construct some examples to show the usefulness of our results. Also, we provide some applications to support our results.
Citation: Wasfi Shatanawi, Taqi A. M. Shatnawi. Some fixed point results based on contractions of new types for extended $ b $-metric spaces[J]. AIMS Mathematics, 2023, 8(5): 10929-10946. doi: 10.3934/math.2023554
The construction of contraction conditions plays an important role in science for formulating new findings in fixed point theories of mappings under a set of specific conditions. The aim of this work is to take advantage of the idea of extended $ b $-metric spaces in the sense introduced by Kamran et al. [A generalization of $ b $-metric space and some fixed point theorems, Mathematics, 5 (2017), 1–7] to construct new contraction conditions to obtain new results related to fixed points. Our results enrich and extend some known results from $ b $-metric spaces to extended b-metric spaces. We construct some examples to show the usefulness of our results. Also, we provide some applications to support our results.
| [1] |
S. Rashid, A. G. Ahmad, F. Jarad, A. Alsaadi, Nonlinear fractional differential equations and their existence via fixed point theory concerning to Hilfer generalized proportional fractional derivative, AIMS Math., 8 (2023), 382–403. https://doi.org/10.3934/math.2023018 doi: 10.3934/math.2023018
|
| [2] |
J. A. Jiddah, M. Noorwali, M. S. Shagari, S. Rashid, F. Jarad, Fixed point results of a new family of hybrid contractions in generalised metric space with applications, AIMS Math., 7 (2022), 17894–17912. https://doi.org/10.3934/math.2022986 doi: 10.3934/math.2022986
|
| [3] |
M. S. Shagari, S. Rashid, F. Jarad, M. S. Mohamed, Interpolative contractions and intuitionistic fuzzy set-valued maps with applications, AIMS Math., 7 (2022), 10744–10758. https://doi.org/10.3934/math.2022600 doi: 10.3934/math.2022600
|
| [4] |
M. Al-Qurashi, M. S. Shagari, S. Rashid, Y. S. Hamed, M. S. Mohamed, Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions, AIMS Math., 7 (2022), 315–333. https://doi.org/10.3934/math.2022022 doi: 10.3934/math.2022022
|
| [5] |
E. Ameer, H. Aydi, M. Arshad, M. De la Sen, Hybrid Ćirić type graphic $\Upsilon, \Lambda$-contraction mappings with applicaions to electric circuit and fractional differential equations, Symmetry, 12 (2020), 1–21. https://doi.org/10.3390/sym12030467 doi: 10.3390/sym12030467
|
| [6] | S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equation int egrals, Fund. Math., 3 (1922), 133–181. |
| [7] |
T. Kamran, M. Samreen, Q. U. Ain, A generalization of $b$-metric space and some fixed point theorems, Mathematics, 5 (2017), 1–7. https://doi.org/10.3390/math5020019 doi: 10.3390/math5020019
|
| [8] | I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., 30 (1989), 26–37. |
| [9] | S. Czerwik, Contraction mappings in $b$-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), 5–11. |
| [10] |
H. P. Huang, G. T. Deng, S. Radevovic, Fixed point theorems in $b$-metric spaces with applications to differential equations, J. Fixed Point Theory Appl., 20 (2018), 1–24. https://doi.org/10.1007/s11784-018-0491-z doi: 10.1007/s11784-018-0491-z
|
| [11] | A. Mukheimer, N. Mlaiki, K. Abodayeh, W. Shatanawi, New theorems on extended $b$-metric spaces under new contractions, Nonlinear Anal. Model. Control, 24 (2019), 870–883. |
| [12] |
W. Shatanawi, A. Pitea, V. Lazovic, Contraction conditions using comparison functions on $b$-metric spaces, Fixed Point Theory Appl., 2014 (2014), 1–11. https://doi.org/10.1186/1687-1812-2014-135 doi: 10.1186/1687-1812-2014-135
|
| [13] |
W. Shatanawi, Z. D. Mitrović, N. Hussain, S. Radenović, On generalized Hardy-Rogers type $\alpha$-admissible mappings in cone $b$-metric spaces over Banach algebras, Symmetry, 12 (2020), 1–12. https://doi.org/10.3390/sym12010081 doi: 10.3390/sym12010081
|
| [14] |
B. Ali, H. A. Butt, M. De la Sen, Existence of fixed points of generalized set-valued $F$-contractions of $b$-metric spaces, AIMS Math., 7 (2022), 17967–17988. https://doi.org/10.3934/math.2022990 doi: 10.3934/math.2022990
|
| [15] |
N. Konwar, P. Debnath, Fixed point results for a family of interpolative $F$-contractions in $b$-metric spaces, Axioms, 11 (2022), 1–10. https://doi.org/10.3390/axioms11110621 doi: 10.3390/axioms11110621
|
| [16] |
H. P. Huang, Y. M. Singh, M. S. Khan, S. Radenović, Rational type contractions in extended $b$-metric spaces, Symmetry, 13 (2021), 1–19. https://doi.org/10.3390/sym13040614 doi: 10.3390/sym13040614
|
| [17] | M. S. Khan, Y. M. Singh, M. Abbas, V. Rakočević, On non-unique fixed point of Ćirić type operators in extended $b$-metric spaces and applications, Rend. Circ. Mat. Palermo Ser. 2, 69 (2020), 1221–1241. https://doi.org/10.1007/s12215-019-00467-4 |
| [18] | T. Abdeljawad, K. Abodayeh, N. Mlaiki, On fixed point generalizations to partial $b$-metric spaces, J. Comput. Anal. Appl., 19 (2015), 883–891. |
| [19] |
W. Shatanawi, Z. Mustafa, N. Tahat, Some coincidence point theorems for nonlinear contraction in ordered metric spaces, Fixed Point Theory Appl., 2011 (2011), 1–15. https://doi.org/10.1186/1687-1812-2011-68 doi: 10.1186/1687-1812-2011-68
|
| [20] |
J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized $(\psi, \varphi)_{s}$-contractive mappings in ordered $b$-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1–23. https://doi.org/10.1186/1687-1812-2013-159 doi: 10.1186/1687-1812-2013-159
|
| [21] |
N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics, 6 (2018), 1–7. https://doi.org/10.3390/math6100194 doi: 10.3390/math6100194
|
| [22] |
M. S. Aslam, M. S. R. Chowdhury, L. Guran, A. Manzoor, T. Abdeljawad, D. Santina, et al., Complex-valued double controlled metric like spaces with applications to fixed point theorems and Fredholm type integral equations, AIMS Math., 8 (2023), 4944–4963. https://doi.org/10.3934/math.2023247 doi: 10.3934/math.2023247
|
| [23] |
Z. H. Ma, J. Ahmad, A. E. Al-Mazrooei, Fixed point results for generalized contractions in controlled metric spaces with applications, AIMS Math., 8 (2023), 529–549. https://doi.org/10.3934/math.2023025 doi: 10.3934/math.2023025
|
| [24] |
A. Shoaib, P. Kumam, S. S. Alshoraify, M. Arshad, Fixed point results in double controlled quasi metric type spaces, AIMS Math., 6 (2021), 1851–1864. https://doi.org/10.3934/math.2021112 doi: 10.3934/math.2021112
|
| [25] | S. S. Aiadi, W. A. M. Othman, K. Wang, N. Mlaiki, Fixed point theorems in controlled $J$-metric spaces, AIMS Math., 8 (2023), 4753–4763. https://doi.org/10.3934/math.2023235 |
| [26] |
M. Farhan, U. Ishtiaq, M. Saeed, A. Hussain, H. A. Sulami, Reich-type and $(\alpha, F)$-contractions in partially ordered double-controlled metric-type paces with applications to non-linear fractional differential equations and monotonic iterative method, Axioms, 11 (2022), 1–17. https://doi.org/10.3390/axioms11100573 doi: 10.3390/axioms11100573
|
Wasfi Shatanawi, Taqi A. M. Shatnawi. Some fixed point results based on contractions of new types for extended $ b $-metric spaces[J]. AIMS Mathematics, 2023, 8(5): 10929-10946. doi: 10.3934/math.2023554
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