In the present paper first we define Soft Metric Space, b-Soft Metric Space, Monotone property and α-Monotone property and then we establish two results. In the first result we prove coupled soft fixed point theorem in ordered soft bmetric space with monotone property. In the second theorem establish coupled soft coincidence fixed point theorem for mapping satisfying generalized contractive conditions with α-monotone property in an ordered soft b-metric space. We also prove the validity of theorem 2.2 with example.

Abstract:In the present paper, we define Coupled Soft Metric Space. In the first part, we establish coupled soft fixed point theorem in soft metric space and in the second part of this paper, we prove coupled soft coincidence fixed point theorem for mapping satisfying generalized contractive conditions with α -monotone property in an ordered soft b-metric space.

In the present paper, we define Dislocated Soft Metric Space and discuss about the existence and uniqueness of soft fixed point of a cyclic mapping in soft dislocated metric space. We also prove the unique soft fixed point theorems of a cyclic mapping in the context of dislocated soft metric space. Examples are given for support of the results.

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In this paper, we prove fixed point theorems for generalized C-contractive and generalized S-contractive mappings in a bi-complete di-metric space. The relationship between q-spherically complete T 0 Ultra-quasi-metric space and bi-complete diametric space is pointed out in proposition 3.2. This work is motivated by Petals and Fvidalis in a T 0 -ultraquasi-metric space