GAZETA MATEMATICA˘ - SSMR

GAZETA MATEMATIC ASERIA AANUL XXXV (CXIV)Nr. 1 2/ 2017 ARTICOLESome results concerning fixed points of -contractionsLoredana Ioana1)Abstract. Existence and uniqueness of fixed points of -contractions, inthe general sense, are given. Three proofs of a variant of the Boyd-Wongtheorem are presented. Using the conclusion of the theorem, some otherresults concerning the attractor of a GIFS of -contractions are :fixed point; Boyd-Wong theorem; :Primary 54H25; Secondary and preliminariesIn the last few decades, fixed point theory has had a very flourishingdevelopment, mainly because of its large range of beginning of the theory was in a certain way the classical Banachtheorem, which states that ifXis a complete metric space andfis a mappingofXinto itself which satisfiesd(f(x), f(y)) d(x, y),for some [0,1) and allx, y X,thenfhas a fixed pointx, and the successive approximationsfn(x) convergetoxforx , the conditiond(f(x), f(y)) d(x, y) does not insure thatfhas a fixed 1969 appeared the theorem of Boyd-Wong, which replaces the con-dition of Banach withd(f(x), f(y)) (d(x, y)), x, y X,where : [0, ) [0, ) is a comparison nition mapping : [0, ) [0, )is called acomparis]]]]]

GAZETA MATEMATICA˘ SERIA A ANUL XXXV (CXIV) Nr. 1 – 2/ 2017 ARTICOLE Some results concerning fixed points of φ-contractions Loredana Ioana1) Abstract. Existence and uniqueness of fixed points of φ-contractions, in the general sense, are given.

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