Some Fixed Point Results in Dislocated Quasi-Metric Space

In this paper we indicate a way to generalize a series of fixed point results in the framework of b-metric spaces and we exemplify it by extending Nadler's contraction principle for set-valued functions (see Multi-valued contraction mappings, Pac. J. Math., 30 (1969), 475-488) and a fixed point theorem for set-valued quasi-contractions functions due to H. Aydi, M.F. Bota, E. Karapinar and S. Mitrović (see A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed

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“…Obviously our Lemma 2.2 is a generalization of the above Lemma which is the corner stone of the results from [16], [18], [19], [22] and [28].…”

Section: Remarks and Commentsmentioning

confidence: 83%

New fixed point theorems for set-valued contractions in b-metric spaces

Miculescu

Mihail

2017

J. Fixed Point Theory Appl.

117

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“…The concept of b-metric introduced by Bakhtin [3] and Czerwik [4] is applied to obtain some fixed point theorems for contraction mappings in a b-metric space. Furthermore, many authors proved fixed point theorems in a b-metric space ( [5][6][7]), and the quasi b-metric space was usually used as a dislocated quasi b-metric space for fixed point theorems [8,9]. Using this idea, we present generalization of some fixed point theorems of Banach type in some generalized b-metric spaces, especially in the quasi αb-metric space.…”

Section: Budi Nurwahyu 1814mentioning

confidence: 99%

FIXED POINT THEOREMS FOR GENERALIZED CONTRACTION MAPPINGS IN QUASI \alpha b-METRIC SPACE

Nurwahyu¹

2017

FJMS

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“…Using this idea researcher presented generalization of the renowned Banach Fixed Point Theorem in the b-metric space for ( [27], [28][29]). Many authers have studied the extension of Fixed Point Theorem in b-metric space, see for instance ([30], [31,32,33], [34], [35], [36], [37] [38], [39], [40,41][42] [43], [44], [45]& [46]& [47]). In 1978, Feisher and khan [9] generalized the Banach Contraction Principle with rational expression and proved some fixed and common fixed point theorems.…”

Section: Imentioning

confidence: 99%