The Journal of the Indian Mathematical Society

S. C. Arora ¹, J. K. Kohli ², Durgesh Kumar ³

Affiliations
1 Department of Mathematics, University of Delhi, Delhi - 110007, IN
2 Department of Mathematics, Hindu College University of Delhi, Delhi - 110007, IN
3 Department of Mathematics, Motilal Nehru College University of Delhi, Delhi - 110021, IN

Abstract

The aim of the present paper is to prove a common fixed point theorem for four mappings in uniform spaces via weakly compatible mappings. This generalizes several known results in the literature.

Keywords

Weakly Compatible Maps, Fixed Point, Cauchy Filter.

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Taddesse Zegeye ¹, S. C. Arora ¹

Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, IN

Abstract

A slant Toeplitz operator A_φ with symbol φ in L^∞(T) where T is the unit circle on the complex plane, is an operator where the representing matrix M=(a_ij) is given by a_ij=<φ,z^2i-j> where is the usual inner product in L²(T). The operator B_φ denotes the compression of A_φ, to H²(T) (Hardy space). In this paper, we prove that the spectrum of B_φ contains a closed disc and the interior of this disc consists of eigenvalues with infinite multiplicity, if T_φ is invertible, where T_φ is the Toeplitz operator on H²(T).

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S. C. Arora ¹, Alpana Rastogi ¹

Affiliations
1 Department of Mathematics, University of Delhi, Delhi 110007, IN

Abstract

A selfmap T on a metric space (X, d) is said to be asymptotically regular [4] at x in X if d(Tⁿx, Tⁿ⁺¹x) → 0 as n → ∞ and is said to be asymptotically regular on X if it is asymptotically regular for each x in X. T is said to be asymptotically bounded [1] on a Banach space X if ||Tⁿ|| ≥ M for some constant M≥ 0 and for all n≥ 1.

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