Abstract

In this paper, we introduce the concept of bipolar 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.

Keywords: Fixed point; bipolar cone$_{tvs}$ $b$-metric space; covariant and contravariant mappings; contravariant $A$-contraction mappings; homotopic mappings.

MSC: 47H10, 54H25

Pages:  281$-$296     

Volume  72 ,  Issue  4 ,  2020