2013
DOI: 10.1155/2013/986028
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Abstract: Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

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Cited by 22 publications
(22 citation statements)
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“…Due to its applications in mathematics and other related disciplines, Banach contraction principle has been generalized in many directions. Extensions of Banach contraction principle have been obtained either by generalizing the domain of the mapping or by extending the contractive condition on the mappings (see, [1,2,3,4,5,6,7,10,11,13,14,15,16,18,19,22,23,24,26,27,28,29,30,31,32,34,35] and references therein).…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Due to its applications in mathematics and other related disciplines, Banach contraction principle has been generalized in many directions. Extensions of Banach contraction principle have been obtained either by generalizing the domain of the mapping or by extending the contractive condition on the mappings (see, [1,2,3,4,5,6,7,10,11,13,14,15,16,18,19,22,23,24,26,27,28,29,30,31,32,34,35] and references therein).…”
Section: Introductionmentioning
confidence: 99%
“…Following this trend, Samet et al [34] first introduced α-admissible mappings and then α-ψ-contractive type mappings to obtain some interesting generalizations of Banach contraction principle. For more results in this direction, we refer to [6,13,14,16,17,20,21,22,24,28,30,32] and references mentioned therein. Recently, Alizadeh et al [5] defined the concept of cyclic (α, β)-admissible mapping as follows: Definition 1.1 ( [5]).…”
Section: Introductionmentioning
confidence: 99%
“…In this section, we consider α-admissible mappings (see Kumam-Vetro-Vetro [14], Samet-Vetro-Vetro [20]) and introduce the notion of α-g-contraction of Perov type in the setting of rectangular cone metric spaces. For this class of contractions, we give again results of existence and uniqueness of points of coincidence and common fixed points.…”
Section: α-Contraction Of Perov Typementioning
confidence: 99%
“…In addition to that they applied the results of their works to matrix equations. Many mathematicians have worked on ordered metric spaces since that time (see for example [4,5]). Nieto and Rodríguez-López [7,8] presented some new results for contractions in ordered metric spaces.…”
Section: Introductionmentioning
confidence: 99%