International Journal of Nonlinear Analysis and Applications
Sequential bipolar metric space and well-posedness of fixed point problems
Document Type : Research Paper
Authors
Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India
Abstract
In this paper, we introduce the concept of sequential bipolar metric spaces which is a generalization of bipolar metric spaces and bipolar b−metric spaces and in view of this concept we prove some fixed point theorems for a class of covariant and contravariant contractive mappings over such spaces. Supporting example have been cited in order to validity of the underlying space. Moreover, our fixed point results are applied to well-posedness of fixed point problems.
Keywords
[1] D. Bajovi´c, Z. D. Mitrovi´c and M. Saha, Remark on contraction principle in conetvs b-metric spaces, J Anal. 29 (2021) 273-–280.
[2] I. Beg, A. K. Laha and M. Saha, Coincidence point of isotone mappings in partially ordered metric space, Rend. Circ. Math. Palermo, (2016), doi:10.1007/S12215016-0232-3.
[3] D. Dey and M. Saha, An extension of Banach fixed point theorem in Fuzzy metric space, Bol. Sociedade Paranaense Mat. 32(1) (2014) 299–304.
[4] D. Dey and M. Saha, Common fixed point theorems in a complete 2-metric space, Acta Univ. Palackianae Olomucensis, Facultas Rerum Naturalium, Math. 52(1) (2013) 79–87.
[5] D. Dey, K. Roy and M. Saha, On generalized contraction principles over S−metric spaces with application to homotopy, J. New Theory, 31 (2020) 95–103.
[6] D. Dey, R. Fierro and M. Saha, Well-posedness of fixed point problems, J. Fixed Point Theory Appl. doi.org/10.1007/s11784-018-0538-i, Springer (2018).
[7] M. Gangopadhyay, A. P. Baisnab and M. Saha, Expansive mappings and their fixed points in a vector metric space, Int. J. Math. Arc. 4(8) (2013) 147–153.
[8] M. Gangopadhyay, M. Saha and A. P. Baisnab, Some fixed point theorems in Partial metric spaces, Turkic World Math. Soc. J. App. Eng. Math. 3(2) (2013) 206–213.
[9] M. Jleli and B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory Appl. (2015), doi:10.1186/s13663-015-0312-7.
[10] A. K. Laha and M. Saha, Fixed point on α − ψ multivalued contractive mappings in cone metric space, Acta Comm. Univ. Tartuensis Math. 20(1) (2016) 35–43.
[11] A. K. Laha and M. Saha, Fixed point for a class of set valued mappings on a metric space endowed with a graph, ROMAI J. 11(1) (2015) 115–129.
[12] A. Mutlu and U. G¨urdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl. 9 (2016) 5362–5373.
[13] A. Mutlu, K. O¨zkan and U. G¨urdal, Coupled fixed point theorems on bipolar metric spaces, European J. Pure Appl. Math. 10(4) (2017) 655–667.
[14] K. Roy, M. Saha and I. Beg, Fixed point of contractive mappings of integral type over an S JS−metric space,
Tamkang J. Math. DOI:10.5556/j.tkjm.52.2021.3298, online published.
[15] K. Roy and M. Saha, Fixed points of mappings over a locally convex topological vector space and Ulam-Hyers stability of fixed point problems, Novi Sad J. Math. 50(1) (2020) 99–112.
[16] K. Roy and M. Saha, Generalized contractions and fixed point theorems over bipolar conetvs b−metric spaces with an application to homotopy theory, Mat. Vesnik, 72(4) (2020) 281–296.
[17] K. Roy and M. Saha, On fixed points of C´iric´-type contractive mappings over a C∗−algebra valued metric space
and Hyers-Ulam stability of fixed point problems, J. Adv. Math. Stud. 12(3) (2019) 350-363.
[18] M. Saha and R. Chikkala, Fixed point theorem over a quasi metric space, South East Asian J. Math. Math. Sci. 8(2) (2010) 61–67.
[2] I. Beg, A. K. Laha and M. Saha, Coincidence point of isotone mappings in partially ordered metric space, Rend. Circ. Math. Palermo, (2016), doi:10.1007/S12215016-0232-3.
[3] D. Dey and M. Saha, An extension of Banach fixed point theorem in Fuzzy metric space, Bol. Sociedade Paranaense Mat. 32(1) (2014) 299–304.
[4] D. Dey and M. Saha, Common fixed point theorems in a complete 2-metric space, Acta Univ. Palackianae Olomucensis, Facultas Rerum Naturalium, Math. 52(1) (2013) 79–87.
[5] D. Dey, K. Roy and M. Saha, On generalized contraction principles over S−metric spaces with application to homotopy, J. New Theory, 31 (2020) 95–103.
[6] D. Dey, R. Fierro and M. Saha, Well-posedness of fixed point problems, J. Fixed Point Theory Appl. doi.org/10.1007/s11784-018-0538-i, Springer (2018).
[7] M. Gangopadhyay, A. P. Baisnab and M. Saha, Expansive mappings and their fixed points in a vector metric space, Int. J. Math. Arc. 4(8) (2013) 147–153.
[8] M. Gangopadhyay, M. Saha and A. P. Baisnab, Some fixed point theorems in Partial metric spaces, Turkic World Math. Soc. J. App. Eng. Math. 3(2) (2013) 206–213.
[9] M. Jleli and B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory Appl. (2015), doi:10.1186/s13663-015-0312-7.
[10] A. K. Laha and M. Saha, Fixed point on α − ψ multivalued contractive mappings in cone metric space, Acta Comm. Univ. Tartuensis Math. 20(1) (2016) 35–43.
[11] A. K. Laha and M. Saha, Fixed point for a class of set valued mappings on a metric space endowed with a graph, ROMAI J. 11(1) (2015) 115–129.
[12] A. Mutlu and U. G¨urdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl. 9 (2016) 5362–5373.
[13] A. Mutlu, K. O¨zkan and U. G¨urdal, Coupled fixed point theorems on bipolar metric spaces, European J. Pure Appl. Math. 10(4) (2017) 655–667.
[14] K. Roy, M. Saha and I. Beg, Fixed point of contractive mappings of integral type over an S JS−metric space,
Tamkang J. Math. DOI:10.5556/j.tkjm.52.2021.3298, online published.
[15] K. Roy and M. Saha, Fixed points of mappings over a locally convex topological vector space and Ulam-Hyers stability of fixed point problems, Novi Sad J. Math. 50(1) (2020) 99–112.
[16] K. Roy and M. Saha, Generalized contractions and fixed point theorems over bipolar conetvs b−metric spaces with an application to homotopy theory, Mat. Vesnik, 72(4) (2020) 281–296.
[17] K. Roy and M. Saha, On fixed points of C´iric´-type contractive mappings over a C∗−algebra valued metric space
and Hyers-Ulam stability of fixed point problems, J. Adv. Math. Stud. 12(3) (2019) 350-363.
[18] M. Saha and R. Chikkala, Fixed point theorem over a quasi metric space, South East Asian J. Math. Math. Sci. 8(2) (2010) 61–67.
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Volume 12, Issue 2
November 2021Pages 387-398
- Receive Date: 13 May 2020
- Accept Date: 15 June 2020