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Sirous Moradi

Academic rank: Assistant Professor
ORCID:
Education: PhD.
ScopusId:
HIndex:
Faculty: Arak University
Address: Arak University
Phone:

Research

Title
On Olaleru’s open problem on Gregus fixed point theorem
Type
JournalPaper
Keywords
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Year
2013
Journal Journal of Global Optimization
DOI
Researchers Sirous Moradi ، Ali Farajzadeh

Abstract

Let (X, d) be a complete metric space and TX⟶X be a mapping with the property d(Tx, Ty) ≤ ad(x, y) + bd(x, Tx) + cd(y, Ty) + ed(y, Tx) + fd(x, Ty) for all x,y∈X , where 0 < a < 1, b, c, e, f ≥ 0, a + b + c + e + f = 1 and b + c > 0. We show that if e + f > 0 then T has a unique fixed point and also if e + f ≥ 0 and X is a closed convex subset of a complete metrizable topological vector space (Y, d), then T has a unique fixed point. These results extend the corresponding results which recently obtained in this field. Finally by using our main results we give an answer to the Olaleru’s open problem.