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In this paper, we study the generalization of the Banach contraction principle in the vector space, involving four rational square terms in the inequality, by using the notation of bilinear functional. We also present an extension of Selberg's inequality to vector space.
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 F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (2) (1967), 197–228. Google Scholar
 L. Debnath and P. Mikusinski, Hilbert Spaces with Applications, Third Edition, Elsevier Aca- demic Press, 2005. Google Scholar
 T. L. Hicks and E. W. Huffman, Fixed point theorems in generalized Hilbert spaces, J. Math. Anal. Appl. 64 (3) (1978), 562–568. Google Scholar
 E. W. Huffman, Strict convexity in locally convex spaces and fixed point theorems, Math. Japon- ica. 22 (1977), 323–333. Google Scholar
 P. V. Koparde and D. B. Waghmode, Kanan Type mappings in Hilbert spaces, Scientist of Physical sciences. 3 (1) (1991), 45–50. Google Scholar
 H. R. Moradi, M. E. Omidvar, and M. K. Anwary, An extension of Kantorovich inequality for sesquilinear maps, Eur. J. Pure Appl. Math. 10 (2) (2017), 231–237. Google Scholar
 H. R. Moradi, M. E. Omidvar, S. S. Dragomir, and M. S. Khan, Sesquilinear version of numerical range and numerical radius, Acta Univ. Sapientiae, Mathematica. 9 (2) (2017), 324–335. Google Scholar
 D. M. Pandhare, On the sequence of mappings on Hilbert space, The Mathematics Education. 32 (2) (1998), 61–63. Google Scholar
 N. S. Rao, K. Kalyani, and N. C. P. Ramacharyulu, Result on fixed point theorem in Hilbert space, Int. J. Adv. Appl. Math. and Mech. 2 (3) (2015), 208–210. Google Scholar
 T. Veerapandi and S. A. Kumar, Common fixed point theorems of a sequence of mappings on Hilbert space, Bull. Cal. Math. Soc. 91 (4) (1999), 299–308. Google Scholar