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Abstract
In this paper, we define the mapping called (ψ, ϕ, ω)-weak contractions. We then use this definition to proof the existence of fixed point. The mapping we defined above is a modified mapping by Liu and Chai. We use the concept ω-distance to proof the fixed point theorem. Since every ω-distance is metric, then the resulting theorem also satisfy for every metric.
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References
- Kada O., Suzuki, T., and Takahashi, W., ”Non convex minimization theorems and fixed point theorems in complete metric spaces”, Math. Japan, 44 (1996), 381-391.
- Kutbi, M. A., and Sintunavarat, W., ”Fixed point theorem for generalized ωα-contraction multivalued mappings in α-complete metric spaces,” Fixed Point Theory Appl., 139 (2014).
- Prasad, G., ”Fixed Point Theorems via ω-Distance in Relational Metric Spaces with an Application,” Filomat, 34 (6) (2020), 1889–1898.
- Pasangka, I. G., “Teorema Titik Tetap Berkaitan dengan Pemetaan Kontraksi-F dan Jarak-w pada Ruang Metrik Lengkap”, Barekeng: Jurnal Ilmu Matematika dan Terapan, 15(2)(2021), 355-360.
- Senapati, T., Dey, L. K., Damjanovic, B., and Chanda, A., ”New fixed point results in orthogonal metric spaces with an application”, Kragujevac Journal of Mathematics, 42 (4)(2018), 505-516.
- Zhang, F., Wang, H., Wu, S., and Zhao, L., ”Fixed-Point Theorems for α-Admissible Mappings with ω-Distance and Applications to Nonlinear Integral Equations”, Mathematical Problems in Engineering, 2020 (2020), 1-7.
- Kari, A., Rossafi, M., Marhrani E. M., and Aamri, M., ”Fixed-point theorem for nonlinear F-contraction via ω-distance”, Advances in Mathematical Physics, 2020 (2020), 1-10.
- Barootkoob, S., and Lakzian, H., ”Fixed point results via L-contractions on quasi ω-distances”, Journal of Mathematical Extension, 15 (2021), 1-22.
- Mongkolkeha, C., and Gopal, D., ”Some common fixed point theorems for generalized F-contraction involving ω-distance with some applications to differential equations”, Mathematics, 7 (32) (2018).
- Romaguera, S., ”ω-Distances on fuzzy metric spaces and fixed points”, Mathematics, 8 (11) (2020).
- Guran, L., Bota, M.-F., and Naseem, A., ”Fixed point problems on generalized metric spaces in Perov’s sense”, Symmetry, 12 (5) (2020).
- Pasangka, I. G., “Teorema Titik Tetap Pemetaan Kontraksi-ψ − ω Bernilai Banyak pada Ruang Metrik Lengkap-α”, Jurnal Sains Dasar, 9(2) (2020), 50-53.
- Lakzian, H., and Samet, B., “Fixed Points for (ψ, ϕ)-Weakly Contractive Mappings in Generalized Metric Spaces”, Applied Mathematics Letters, 25(5) (2012), 902-906.
- Liu, B., and Chai, G. Q., “Fixed Points Theorem for Weakly Contractive Mappings in Generalized Metric Spaces”, Hubei Shifan Xueyuan Xuebao, 33(1) (2013), 60-65.
- Xue, Z., and Lv, G., “A Fixed Point Theorem for Generalized (ψ, ϕ)-Weak Contractions in Branciari Type Generalized Metric Spaces”, Fixed Point Theory and Algorithms for Sciences and Engineering, 2021(1) (2021), 1-13.
References
Kada O., Suzuki, T., and Takahashi, W., ”Non convex minimization theorems and fixed point theorems in complete metric spaces”, Math. Japan, 44 (1996), 381-391.
Kutbi, M. A., and Sintunavarat, W., ”Fixed point theorem for generalized ωα-contraction multivalued mappings in α-complete metric spaces,” Fixed Point Theory Appl., 139 (2014).
Prasad, G., ”Fixed Point Theorems via ω-Distance in Relational Metric Spaces with an Application,” Filomat, 34 (6) (2020), 1889–1898.
Pasangka, I. G., “Teorema Titik Tetap Berkaitan dengan Pemetaan Kontraksi-F dan Jarak-w pada Ruang Metrik Lengkap”, Barekeng: Jurnal Ilmu Matematika dan Terapan, 15(2)(2021), 355-360.
Senapati, T., Dey, L. K., Damjanovic, B., and Chanda, A., ”New fixed point results in orthogonal metric spaces with an application”, Kragujevac Journal of Mathematics, 42 (4)(2018), 505-516.
Zhang, F., Wang, H., Wu, S., and Zhao, L., ”Fixed-Point Theorems for α-Admissible Mappings with ω-Distance and Applications to Nonlinear Integral Equations”, Mathematical Problems in Engineering, 2020 (2020), 1-7.
Kari, A., Rossafi, M., Marhrani E. M., and Aamri, M., ”Fixed-point theorem for nonlinear F-contraction via ω-distance”, Advances in Mathematical Physics, 2020 (2020), 1-10.
Barootkoob, S., and Lakzian, H., ”Fixed point results via L-contractions on quasi ω-distances”, Journal of Mathematical Extension, 15 (2021), 1-22.
Mongkolkeha, C., and Gopal, D., ”Some common fixed point theorems for generalized F-contraction involving ω-distance with some applications to differential equations”, Mathematics, 7 (32) (2018).
Romaguera, S., ”ω-Distances on fuzzy metric spaces and fixed points”, Mathematics, 8 (11) (2020).
Guran, L., Bota, M.-F., and Naseem, A., ”Fixed point problems on generalized metric spaces in Perov’s sense”, Symmetry, 12 (5) (2020).
Pasangka, I. G., “Teorema Titik Tetap Pemetaan Kontraksi-ψ − ω Bernilai Banyak pada Ruang Metrik Lengkap-α”, Jurnal Sains Dasar, 9(2) (2020), 50-53.
Lakzian, H., and Samet, B., “Fixed Points for (ψ, ϕ)-Weakly Contractive Mappings in Generalized Metric Spaces”, Applied Mathematics Letters, 25(5) (2012), 902-906.
Liu, B., and Chai, G. Q., “Fixed Points Theorem for Weakly Contractive Mappings in Generalized Metric Spaces”, Hubei Shifan Xueyuan Xuebao, 33(1) (2013), 60-65.
Xue, Z., and Lv, G., “A Fixed Point Theorem for Generalized (ψ, ϕ)-Weak Contractions in Branciari Type Generalized Metric Spaces”, Fixed Point Theory and Algorithms for Sciences and Engineering, 2021(1) (2021), 1-13.