Pranati Maity - Academia.edu (original) (raw)
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Papers by Pranati Maity
In the present work the use of ternary relations is introduced in fixed point theory to obtain so... more In the present work the use of ternary relations is introduced in fixed point theory to obtain some fixed point results in G-metric spaces. Amongst several generalizations of metric spaces suggested in recent times, G-metric spaces are the ones in which the metric is replaced by a function through which sets of three elements are assigned to non-negative real numbers. A ternary relation is assumed on the space and a generalized contractive condition is assumed for the triplets of elements related by the ternary relation. Fixed point and related results are established for such contractions as generalization of contractive mapping principle. The case without the assumption of ternary relation on the space is also discussed. There are some corollaries and illustrative examples. The illustrations establish the actuality of the generalization. The methodology of the proofs are new in the context of G-metric spaces.
The Journal of Nonlinear Sciences and Applications, 2017
In this paper we establish best proximity point results for monotone multivalued mappings in part... more In this paper we establish best proximity point results for monotone multivalued mappings in partially ordered metric spaces. We consider three notions of monotonicity of multivalued mappings. The main theorem is obtained by utilizing property UC and MT-functions. There is no requirement of continuity on the multivalued function which is illustrated with two supporting examples of the results established in this paper. There are two corollaries. Some existing results are extended to the domain of partially ordered metric spaces through one of the corollaries.
Journal of Operators, 2014
Putting several existing ideas together, in this paper we define the concept of cyclic coupled Ka... more Putting several existing ideas together, in this paper we define the concept of cyclic coupled Kannan type contraction. We establish a strong coupled fixed point theorem for such mappings. The theorem is supported with an illustrative example.
In the present work the use of ternary relations is introduced in fixed point theory to obtain so... more In the present work the use of ternary relations is introduced in fixed point theory to obtain some fixed point results in G-metric spaces. Amongst several generalizations of metric spaces suggested in recent times, G-metric spaces are the ones in which the metric is replaced by a function through which sets of three elements are assigned to non-negative real numbers. A ternary relation is assumed on the space and a generalized contractive condition is assumed for the triplets of elements related by the ternary relation. Fixed point and related results are established for such contractions as generalization of contractive mapping principle. The case without the assumption of ternary relation on the space is also discussed. There are some corollaries and illustrative examples. The illustrations establish the actuality of the generalization. The methodology of the proofs are new in the context of G-metric spaces.
The Journal of Nonlinear Sciences and Applications, 2017
In this paper we establish best proximity point results for monotone multivalued mappings in part... more In this paper we establish best proximity point results for monotone multivalued mappings in partially ordered metric spaces. We consider three notions of monotonicity of multivalued mappings. The main theorem is obtained by utilizing property UC and MT-functions. There is no requirement of continuity on the multivalued function which is illustrated with two supporting examples of the results established in this paper. There are two corollaries. Some existing results are extended to the domain of partially ordered metric spaces through one of the corollaries.
Journal of Operators, 2014
Putting several existing ideas together, in this paper we define the concept of cyclic coupled Ka... more Putting several existing ideas together, in this paper we define the concept of cyclic coupled Kannan type contraction. We establish a strong coupled fixed point theorem for such mappings. The theorem is supported with an illustrative example.