The Journal of the Indian Mathematical Society

Saurabh Manro ¹, Sanjay Kumar ², S. S. Bhatia ¹

Affiliations
1 School of Mathematics and Computer Applications, Thapar University, Patiala-147004, IN
2 Deenbandhu Chhotu Ram University of Science and Technology Murthal (Sonepat), IN

Abstract

In this paper, employing the common (E.A) like property,we prove a common fixed theorem for weakly compatible mappings via an implicit relation in intuitionistic fuzzy metric space.

Keywords

Intuitionistic Fuzzy Metric Space, Weakly Compatible Mappings, Common (E.A) Like Property, Implicit Relation.

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Dinesh Kumar ¹, Gopal Datt ¹, Sanjay Kumar ²

Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110 007, IN
2 Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi, New Delhi-110 015, IN

Abstract

It is known that the dynamics of f and g vary to a large extent from that of its composite entire functions. Using Approximation theory of entire functions, we have shown the existence of entire functions f and g having infinite number of domains satisfying various properties and relating it to their composition. We have explored and enlarged all the maximum possible ways of the solution in comparison to the past result worked out.

Keywords

Fatou Set, Wandering Domain, Carleman Set, Preperiodic Domain.

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Sanjay Kumar ¹

Affiliations
1 Deenbandhu Chhotu Ram University of Science and Technology, Murthal, Sonepat, Haryana, IN

Abstract

In this paper, common fixed point theorems for different variants of R-weak commutative mappings in fuzzy metric spaces have been established and these maps do not force the map to be continuous at the fixed point.

Keywords

Fuzzy Metric Spaces, Variants of R-Weak Commutativity Mappings (R-Weak Commutativity of Type (AG) Mappings, R-Weak Commutativity of Type (AF) Mappings, R-Weak Commutativity of Type (P) Mappings).

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Renu Chugh ¹, Sanjay Kumar ¹

Affiliations
1 Department of Mathematics, Maharshi Dayanand University, Rohtak-124001, IN

Abstract

The purpose of this paper is to prove a common fixed point theorem, from the class of compatible continuous mappings to a larger class of mappings having non-compatible and discontinuous mappings, which generalizes the result of Jungck, Fisher, Kang and Kim, Jachymski, Rhoades and Pant.

Keywords

R-Weak Commutativity, Reciprocal Continuity, Compatible Mappings.

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Sanjay Kumar ¹, Nand Lal ²

Affiliations
1 Department of Mathematics, Deen Dayal Upadhyaya College, Delhi University, New Delhi-110 015, IN
2 Department of Mathematics, Banaras Hindu University, Varanasi-221005, IN

Abstract

Let B(l²) be the C*-algebra of all bounded linear operators on the Hilbert space l² of square-summable sequences of complex numbers. It is known [1, 5, 6] that every non-zero derivation on B(l²) is non-compact. In this paper we investigate the polynomial compactness of some derivations on B(l²).

Keywords

C*-Algebra, Polynomial Compactness, Inner Derivation, Weighted Shift Operator.

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