2015
DOI: 10.22436/jnsa.008.06.19
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On Suzuki-Wardowski type fixed point theorems

Abstract: Recently, Piri and Kumam [Fixed Point Theory and Applications 2014, 2014:210] improved concept of Fcontraction and proved some Wardowski and Suzuki type fixed point results in metric spaces. The aim of this article is to define generalized α−GF-contraction and establish Wardowski and Suzuki type fixed point results in metric and ordered metric spaces and derive main results of Piri et al. as corollaries. We also deduce certain fixed and periodic point results for orbitally continuous generalized F-contractions… Show more

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Cited by 52 publications
(27 citation statements)
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“…It is widely known that the Banach contraction principle [1] is the first metric fixed point theorem and one of the most powerful and versatile results in the field of functional analysis. Due to its significance and several applications, over the years, it has been generalized in different directions by several mathematicians (for example, see ( [2,3,4,5,7,10,17,18,15,16,19]) and references therein).…”
Section: Introductionmentioning
confidence: 99%
“…It is widely known that the Banach contraction principle [1] is the first metric fixed point theorem and one of the most powerful and versatile results in the field of functional analysis. Due to its significance and several applications, over the years, it has been generalized in different directions by several mathematicians (for example, see ( [2,3,4,5,7,10,17,18,15,16,19]) and references therein).…”
Section: Introductionmentioning
confidence: 99%
“…Later on many authors generalized this result in a different way in various generalized metric spaces. For more details in this direction we refer the reader to [1,3,2,6,8,10].…”
Section: Common Fixed Point Results For F-contractionmentioning
confidence: 99%
“…For more details on F-contraction, we refer the reader to [3,4,[19][20][21][22][23]28]. On the other hand, Heilpern [18] used the concept of fuzzy set to introduced a class of fuzzy mappings, which is a generalization of the set-valued mapping, and proved a fixed point theorem for fuzzy contraction mappings in metric linear space in 1981.…”
Section: D(t X T Y) λD(x Y) + L Min{d(x T X) D(y T Y) D(x T Y)mentioning
confidence: 99%