Fixed point theorems in ordered metric spaces via w-distances

Imdad, Mohammad; Rouzkard, Fayyaz

doi:10.1186/1687-1812-2012-222

Cited by 16 publications

(11 citation statements)

References 8 publications

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“…But, here we limit ourselves to only those conditions which correspond to Examples 2.1, 2.2 and 2.3 yielding thereby the refined and sharpened versions of some fixed point theorems contained in Singh and Chauhan [28], Imdad et al [11], Mishra et al [19] besides some other ones which can be stated as under: By setting A = B in Theorem 3.1, we derive the following corollary for three mappings. for all x, y ∈ X, F ∈ F 6 and for all s > 0.…”

Section: Resultsmentioning

confidence: 99%

“…A pair (A, S) of self mappings of a fuzzy metric space (X, M, ) is said to be weakly commuting if M(ASx, S Ax, t) ≥ M(Ax, Sx, t) for every x in X and t > 0. Definition 1.6 [11,22]. A pair of self-mappings (A, S) of a fuzzy metric space (X, M, ) is said to be compatible (or asymptotically commuting) if for all t > 0, limit n→∞ M(ASx n , S Ax n , t) = 1, whenever {x n } is a sequence in X such that…”

Section: Introductionmentioning

confidence: 99%

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Some new common fixed point theorems in fuzzy metric spaces

Gopal

Imdad

2011

Ann Univ Ferrara

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The purpose of this paper is to prove some new common fixed point theorems in (GV )-fuzzy metric spaces. While proving our results, we utilize the idea of compatibility due to Jungck (Int J Math Math Sci 9:771-779, 1986) together with subsequentially continuity due to Bouhadjera and Godet-Thobie (arXiv: 0906.3159v1 [math.FA] 17 Jun 2009) respectively (also alternately reciprocal continuity due to Pant (Bull Calcutta Math Soc 90:281-286, 1998) together with subcompatibility due to Bouhadjera and Godet-Thobie (arXiv:0906.3159v1 [math.FA] 17 Jun 2009) as patterned in Imdad et al. (doi:10.1016/j.aml.2011.01.045) wherein conditions on completeness (or closedness) of the underlying space (or subspaces) together with conditions on continuity in respect of any one of the involved maps are relaxed. Our results substantially generalize and improve a multitude of relevant common fixed point theorems of the existing literature in metric as well as fuzzy metric spaces which include some relevant results due

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some new common fixed point theorems in fuzzy metric spaces

Gopal

Imdad

2011

Ann Univ Ferrara

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“…In 1996, Kada et al [3] introduced the notion of w-distance and elaborated with the help of examples, that the concept of w-distance is general than that of metric on a nonempty set. Several researchers [4][5][6][7] used this notion to obtain some fixed point results not only in usual metric spaces but also in other spaces.…”

Section: Introductionmentioning

confidence: 99%

Fixed-Point Theorems for α-Admissible Mappings with w-Distance and Applications to Nonlinear Integral Equations

Zhang

Wang

et al. 2020

Mathematical Problems in Engineering

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Two fixed-point theorems for α-admissible mappings satisfying contractive inequality of integral type with w-distance in complete metric spaces are proved. Our results extend and improve a few existing results in the literature. As applications, we use the fixedpoint theorems obtained in this paper to establish solvability of nonlinear integral equations. Examples are included. en, T has a fixed point.

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“…Later, Shioji et al [19] studied the relationship between weakly contractive mappings and weakly Kannan mappings under the conditions, the w-distance and the symmetric wdistance. In 2012, Imdad and Rouzkard [13] proved some fixed point theorems in a complete metric space equipped with a partial ordering via the w-distance.…”

Section: Introductionmentioning

confidence: 99%