Rommel Gregorio - Academia.edu (original) (raw)
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Papers by Rommel Gregorio
Advances in Fixed Point Theory, 2013
In this paper, we prove new fixed point theorems of multivalued mappings in partially ordered met... more In this paper, we prove new fixed point theorems of multivalued mappings in partially ordered metric spaces using newly reformulated pre-order relations. As consequence, we derive fixed point theorems for single valued mappings given by Nieto and Rodriguez-Lopez [11], [12]. We also establish some results on the stability of fixed point sets of multivalued mappings in partially ordered metric spaces. General illustrative examples are also given. Essential to our results are the pre-order relations <1,<2,<3defined in [3], and newly reformulated pre-order relations namely <4,<5,<6, which are obtained by imposing a distance condition to comparable elements of two non-empty, closed and bounded sets.
Matthews (1994) introduced the concept of nonzero self-distance called a partial metric and exten... more Matthews (1994) introduced the concept of nonzero self-distance called a partial metric and extended the Banach contraction principle in the context of partial metrics paces. This was followed by Aydi et al. (2012) by extending Nadler’s fixed point theorem to partial metric spaces and introducing the concept of partial Hausdorff metric. In this paper, we prove some fixed point theorems in the context of partial metric spaces endowed with partial ordering using partial Hausdorff metric and a notion of monotone multivalued mappings. Moreover, an example is provided to illustrate the usability of our results.
In this paper we prove coupled fixed point theorems of multivalued mappings in partially ordered ... more In this paper we prove coupled fixed point theorems of multivalued mappings in partially ordered metric spaces by utilizing the combination of multivalued monotone iterative technique and multivalued contraction principle. We also establish some results on the stability of coupled fixed point sets of multivalued mappings in partially ordered metric spaces.
Advances in Fixed Point Theory, Sep 30, 2014
Advances in Fixed Point Theory, 2013
In this paper, we prove new fixed point theorems of multivalued mappings in partially ordered met... more In this paper, we prove new fixed point theorems of multivalued mappings in partially ordered metric spaces using newly reformulated pre-order relations. As consequence, we derive fixed point theorems for single valued mappings given by Nieto and Rodriguez-Lopez [11], [12]. We also establish some results on the stability of fixed point sets of multivalued mappings in partially ordered metric spaces. General illustrative examples are also given. Essential to our results are the pre-order relations <1,<2,<3defined in [3], and newly reformulated pre-order relations namely <4,<5,<6, which are obtained by imposing a distance condition to comparable elements of two non-empty, closed and bounded sets.
Matthews (1994) introduced the concept of nonzero self-distance called a partial metric and exten... more Matthews (1994) introduced the concept of nonzero self-distance called a partial metric and extended the Banach contraction principle in the context of partial metrics paces. This was followed by Aydi et al. (2012) by extending Nadler’s fixed point theorem to partial metric spaces and introducing the concept of partial Hausdorff metric. In this paper, we prove some fixed point theorems in the context of partial metric spaces endowed with partial ordering using partial Hausdorff metric and a notion of monotone multivalued mappings. Moreover, an example is provided to illustrate the usability of our results.
In this paper we prove coupled fixed point theorems of multivalued mappings in partially ordered ... more In this paper we prove coupled fixed point theorems of multivalued mappings in partially ordered metric spaces by utilizing the combination of multivalued monotone iterative technique and multivalued contraction principle. We also establish some results on the stability of coupled fixed point sets of multivalued mappings in partially ordered metric spaces.
Advances in Fixed Point Theory, Sep 30, 2014