On new types of contraction mappings in bipolar metric spaces and applications

الموضوعات :

G. N. V. Kishore ¹ , H. Işık ² , H. Aydi ³ , B. S. Rao ⁴ , D. R. Prasad ⁵

1 - Department of Engineering Mathematics, SRKR Engineering College, Bhimavaram, Andhra Pradesh, 532410, India
2 - Department of Engineering Basic Science, Band\i rma Onyedi Eyl\"{u}l University, 10200 Band\i rma, Bal\i kesir, Turkey
3 - Universit\'e de Sousse, Institut Sup\'erieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
4 - Department of Mathematics, Dr. B.R. Ambedkar University, Srikakulam Andhra Pradesh, 532410, India
5 - Department of Mathematics, K. L. University, Vaddeswaram, Guntur-522 502, Andhra Pradesh, India

تاريخ الإرسال : 27 الأحد , رجب, 1441 تاريخ التأكيد : 20 الجمعة , ربيع الأول, 1442 تاريخ الإصدار : 16 الثلاثاء , ربيع الثاني, 1442

الکلمات المفتاحية: completeness and fixed point, $lambda$-admissible mapping, $lambda-(chi, zeta)$-type contraction mapping,

ملخص المقالة :

Our aim is to present some common fixed point theorems in bipolar metric spaces via certain contractive conditions. Some examples have been provided to illustrate the effectiveness of new results. At the end, we give two applications dealing with homotopy theory and integral equations.

المصادر:

[1] N. Alamgir, Q. Kiran, H. Isik, H. Aydi, Fixed point results via a Hausdorff controlled type metric, Adv. Differ. Equ. 2020, 2020:24.

[2] A. Ali, H. Isik, H. Aydi, E. Ameer, J. R. Lee, M. Arshad, On multivalued Suzuki-type θ-contractions and related applications, Open Mathematics. 18 (1) (2020), 386-399.

[3] S. Alizadeh, F. Moradlou, P. Salimi, Some fixed point results for (α,β)−(ψ,ϕ)-contractive mappings, Filomat. 28 (3) (2014), 635-647.

[4] A. Al-Rawashdeh, H. Aydi, A. Felhi, S. Sahmim, W. Shatanawi, On common fixed points for α-F-contractions and applications, J. Nonlinear Sci. Appl. 9 (5) (2016), 3445-3458.

[5] E. Ameer, H. Aydi, M. Arshad, H. Alsamir, M. S. Noorani, Hybrid multivalued type contraction mappings in α K -complete partial b-metric spaces and applications, Symmetry. 2019, 11, 86.

[6] H. Aydi, A. Felhi, On best proximity points for various α-proximal contractions on metric-like spaces, J. Nonlinear Sci. Appl. 9 (8) (2016), 5202-5218.

[7] A. Felhi, H. Aydi, D. Zhang, Fixed points for α-admissible contractive mappings via simulation functions, J. Nonlinear Sci. Appl. 9 (10) (2016), 5544-5560.

[8] H. Isik, C. Park, Existence of a common solution to systems of integral equations via fixed point results, Open Mathematics. 18 (1) (2020), 249-261.

[9] H. Isik, B. Samet, C. Vetro, Cyclic admissible contraction and applications to functional equations in dynamic programming, Fixed Point Theory Appl. 2015, 2015:163.

[10] H. Isik, D. Turkoglu, Fixed point theorems for weakly contractive mappings in partially ordered metric-like spaces, Fixed Point Theory Appl. (2013), 2013:51.

[11] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthy. 83 (1976), 261-263.

[12] H. Kaddouri, H. I¸ sık, S. Beloul, On new extensions of F-contraction with application to integral inclusions, U.P.B. Sci. Bull. (Series A). 81 (3) (2019), 31-42.

[13] R. Kannan, Some remarks on fixed points, Bull. Calcutta Math. Soc. 10 (1968), 71-76.

[14] G. N. V. Kishore, R. P. Agarwal, B. S. Rao, R. V. N. Srinivasa Rao, Caristi type cyclic contraction and common fixed point theorems in bipolar metric spaces with applications, Fixed Point Theory Appl. 2018, 2018:21.

[15] G. N. V. Kishore, K. P. R. Rao, H. Isik, B. S. Rao, A. Sombabu, Covarian mappings and coupled fixed point results in bipolar metric spaces, Int. J. Nonlinear Anal. Appl. 12 (1) (2021), 1-15.

[16] Z. Mitrovic, H. Isik, S. Radenovic, The new results in extended b-metric spaces and applications, Int. J. Nonlinear Anal. Appl. 11 (1) (2020), 473-482.

[17] F. Moradlou, P. Salimi, P. Vetro, Fixed point results for r − (η,ξ,ψ)-contractive mappingss of type (I), (II) and (III), Filomat. 27 (2013), 403-410.

[18] A. Mutlu, U. Gürdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl. 9 (2016), 5362-5373.

[19] A. Mutlu, K. Ozkan, U. Gürdal, Coupled fixed point theorems on bipolar metric spaces, European J. Pure Appl. Math. 10 (4) (2017), 655-667.

[20] B. S. Rao, G. N. V. Kishore, S. R. Rao, Fixed point theorems under new Caristi type contraction in bipolar metric space with applications, Inter. J. of Engin & Tech. 7 (3.31) (2017), 106-110.

[21] N. Saleem, J. Vujakovic, W. U. Baloch, S. Radenovic, Coincidence point results for multivalued Suzuki type mappings using θ−contraction in b−metric spaces, Mathematics. 2019, 7, 1017.

[22] N. Saleem, M. Abbas, B. Ali, Z. Raza, Fixed points of Suzuki-type generalized multivalued (f,θ,L)−almost contractions with applications, Filomat. 33 (2) (2019), 499-518.

[23] N. Saleem, M. Abbas, Z. Raza, Fixed fuzzy point results of generalized Suzuki type F-contraction mappings in ordered metric spaces, Georgian Math. J. 27(2) (2017), 307-320.

[24] P. Salimi, A. Latif, N. Hussain, Modified α − ψ-contractive mappings with applications, Fixed Point Theory Appl. 2013, 2013:151.

[25] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α−ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.