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We also establish some fixed point theorems for such maps and give an example to illustrate our results.
The notion of semi-weak time consistency for stochastic processes, introduced next, is well suited for scale-invariant maps; we refer the reader to (Bielecki et al. 2014b) for a detailed discussion on time consistency for such maps and their dual representations.13.13
We prove the existence and uniqueness of a fixed point for such mapping in the context of complete metric space.
Lakshimikantham and Ćirić [12] extended the results in [11] by defining the mixed g-monotone and to study the existence and uniqueness of coupled coincidence point for such mapping which satisfy the mixed monotone property in partially ordered metric space.
However, we impose subtle restrictions to obtain fixed point results for such mapping.
For such mapping, we considered only the state in which the first author was bound.
Using this generalized distance, Suzuki and Takahashi [9] have introduced notions of single-valued and multivalued weakly contractive maps and proved fixed point results for such maps.
Later, an interesting and rich fixed point theory for such maps was developed which has applications in control theory, convex optimization, differential inclusion and economics (see [11] and references cited therein).
Later, an interesting and rich fixed point theory for such maps was developed which has found applications in control theory, convex optimization, differential inclusion and economics (see [7] and references therein).
Suzuki and Takahashi [11] introduced single-valued and multi-valued weakly contractive maps with respect to w-distance and proved fixed point results for such maps.
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