# IJPAM: Volume 109, No. 3 (2016)

**SOME FIXED POINT THEOREMS ON THE SUM AND**

PRODUCT OF OPERATORS IN TENSOR PRODUCT SPACES

PRODUCT OF OPERATORS IN TENSOR PRODUCT SPACES

Dipankar Das, Nilakshi Goswami

Department of Mathematics

Gauhati University

Guwahati, 14, Assam, INDIA

Department of Mathematics

Gauhati University

Guwahati, 14, Assam, INDIA

**Abstract.**Let and be Banach spaces and and be two subsets of and respectively. Let and be two mappings and be a self mapping on . Using and we define a self mapping on . Different conditions under which has a fixed point in are established here. Analogous results are also established taking the pair as contraction mappings. Again considering as a reflexive Banach space. We derive the conditions for for having a fixed point in . Some iteration schemes converging to a fixed point of in are also presented here.

**Received:**May 5, 2016

**Revised:**August 27, 2016

**Published: **October 1, 2016

**AMS Subject Classification: **46B28, 47A80, 47H10

**Key Words and Phrases: **projective tensor norm, reflexive tensor product, demiclosed mapping
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# .

**DOI: 10.12732/ijpam.v109i3.13**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2016

**Volume:**109

**Issue:**3

**Pages:**651 - 663

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