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M. M. Taqui Khan ¹, R. P. Pant ¹, K. Venkatasubramanian ¹, R. V. Mehta ²

Affiliations
1 Central Salt & Marine Chemicals Research Institute, Bhavnagar 364002, IN
2 Department of Physics, Bhavnagar University, Bhavnagar 364002, IN

Abstract

The use of Eyring's equation to explain the rate of evaporation of a water based ferrofluid at various temperatures under the influence of magnetic fields of different strengths has yielded information on the changes of entropy and enthalpy of the system. The observed data has been interpreted through the use of a model and a proposed mechanism.

Keywords

Rate of Evaporation, ferrofluid, Applied Magnetic Field.

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R. P. Pant ¹, D. Arora ¹, R. K. Bisht ¹

Affiliations
1 Department of Mathematics, D.S.B. Campus, Kumaun University, Nainital 263 002, IN

Abstract

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 .

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R. P. Pant ¹, K. Jha ², A. B. Lohani ¹

Affiliations
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

Abstract

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.

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R. P. Pant ¹

Affiliations
1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263002, Uttaranchal, IN

Abstract

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.

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R. P. Pant ¹, Vyomesh Pant ¹, A. B. Lohani ¹

Affiliations
1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263002, IN

Abstract

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].

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R. P. Pant ¹

Affiliations
1 Department of Mathematics, Kumaun University, D.S.B. Campus, Nainital-263 002, Uttaranchal, IN

Abstract

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.

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R. P. Pant ¹

Affiliations
1 Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital-263 002 Uttaranchal, IN

Abstract

In the present paper we compare various Meir-Keeler type contractive definitions. By considering the common features of various contractive definitions we introduce some new contractive definitions which on using standard type assumptions and argument will yield new fixed point theorems. The paper opens up scope for the study of a large class of interesting Meir-Keeler type contractive definitions and their associated fixed point theorems.

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Akhilesh Dwivedi ¹, R. P. Pant ², Durgesh Pant ³, Martand Pande , Senam Pandey

Affiliations
1 DSB Campus Kumaon University, Nainital, IN
2 Deptt of Mathematics, DSB Campus, Kumaon University, IN
3 Deptt of Science and Technology, Uttarakhand Science Education and Research Centre (USERC), IN

Abstract

Cloud Computing is the emerging trend to process different types of data and provide different services, and Big data is the huge source of such data. In this paper we proposed a framework in which we encrypt data with clock timing and then provide access according to task and role of the user. By this we can achieve a full secured and authorized access to cloud user with secure big data user.

Keywords

Big Data, Cloud Computing, RBAC, Task, SCT Encryption.

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