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Pant, R. P.
- Induced Metrics and Comparison of Contraction Mappings
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1 Department of Mathematics, D.S.B. Campus, Kumaun University, Nainital 263 002, IN
1 Department of Mathematics, D.S.B. Campus, Kumaun University, Nainital 263 002, IN
Source
The Journal of the Indian Mathematical Society, Vol 76, No 1-4 (2009), Pagination: 119-128Abstract
In this paper we introduce a class of metrics induced by a contraction mapping of a complete metric space and compare three well known contraction definitions in the setting of generalized induced metrics. Our work provides an interesting criterion for further comparison and categorization of generalized contractions into classes of contraction definitions that imply each other in the setting of induced metrics.Keywords
Fixed Points Theorems, Metric Spaces .- Generalization of a Meir-Keeler Type Fixed Point Theorem
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1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263002, Uttaranchal, IN
2 Department of Mathematical Sciences, Kathmandu University, P.O. Box-6250, Kathmandu, NP
1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263002, Uttaranchal, IN
2 Department of Mathematical Sciences, Kathmandu University, P.O. Box-6250, Kathmandu, NP
Source
The Journal of the Indian Mathematical Society, Vol 70, No 1-4 (2003), Pagination: 57-65Abstract
The aim of the present paper is to obtain a fixed point theorem for a sequence of mappings satisfying a weak form of Meir-Keeler type (ε,δ)- contractive condition together with a (Φ-contractive condition without assuming any additional conditions on δ and Φ. The present theorem extends and unifies the Meir-Keeler type and a Φ-contractive type fixed point theorems.- Fixed Point Theorems and Dynamics of Functions
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Authors
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1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263002, Uttaranchal, IN
1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263002, Uttaranchal, IN
Source
The Journal of the Indian Mathematical Society, Vol 70, No 1-4 (2003), Pagination: 135-143Abstract
In the present paper we obtain a common fixed point theorem under a new contractive condition which is independent of the known contractive definitions. In the second fixed point theorem we study the dynamics of a class of functions induced by real numbers and then apply the result to obtain general tests for divisibility of numbers.- Reciprocal Continuity and Common Fixed Points
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Authors
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1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263002, IN
1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263002, IN
Source
The Journal of the Indian Mathematical Society, Vol 70, No 1-4 (2003), Pagination: 157-167Abstract
While studying the fixed point theorems for four mappings A, B, S and T (say) a Meir-Keeler type (ε,δ) contractive condition alone is not sufficient unless some additional condition is imposed on δ or a ∅-contractive condition is also used together with it. In the following pages we prove two common fixed theorems assuming a Meir-Keeler type (ε,δ) contractive condition together with a plane contractive condition (Theorem 1) or Lipschitz type analogue of a plane contractive condition (Theorem 2); however, without imposing any additional restriction on δ or having a ∅-contractive condition used together with it. Simultaneously, we also show that none of the mappings involved in the following theorems is continuous at their common fixed point Thus we not only generalize the Meir-Keeler type and Boyd-Wong type fixed point theorems, but also provide one more answer to the problem (see Rhoades [22]) on the existence of a contractive definition, which is strong enough to generate a fixed point but does not force the map to be continuous at the fixed point. Our result extends the result of Pant [15].- Non-Expansive Mappings and Meir-Keller Type Conditions
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Authors
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1 Department of Mathematics, Kumaun University, D.S.B. Campus, Nainital-263 002, Uttaranchal, IN
1 Department of Mathematics, Kumaun University, D.S.B. Campus, Nainital-263 002, Uttaranchal, IN
Source
The Journal of the Indian Mathematical Society, Vol 71, No 1-4 (2004), Pagination: 239-244Abstract
We obtain fixed point theorems for generalized non-expansive mappings in metric spaces by employing Meir-Keeler type conditions. Our results open up the unexplored area of fixed points of non-expansive self-mappings of metric spaces for investigation. The method developed by us also provides a new tool to deal with non-expansive mappings in Banach spaces.- A Comparison of Contractive Definitions
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Authors
Affiliations
1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263 002 Uttaranchal, IN
1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263 002 Uttaranchal, IN