Generalized contractions and fixed point theorems over bipolar \(\mathrm{cone}_{tvs}\) \(b\)-metric spaces with an application to homotopy theory. (English) Zbl 1488.54170

Roy, Kushal; Saha, Mantu

Mat. Vesn. 72, No. 4, 281-296 (2020).

Summary: In this paper, we introduce the concept of bipolar \(\mathrm{cone}_{tvs}\) \(b\)-metric space and prove some generalized fixed point theorems on it. These theorems extend and generalize some recent results obtained by other authors for mappings on a bipolar metric space. Also, a brief study on topological properties of this newly introduced space has been made and in support of our theorems, we give some examples. Moreover, our fixed point result is applied to homotopy theory on such spaces.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54E40	Special maps on metric spaces

Keywords:

fixed point; bipolar \(\mathrm{cone}_{tvs}\) \(b\)-metric space; covariant and contravariant mappings; contravariant \(A\)-contraction mappings; homotopic mappings

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