Fixed-point theorems in partially ordered metric spaces for operators with PPF dependence

Drici, Z.; McRae, F.A.; Devi, J. Vasundhara

doi:10.1016/j.na.2006.06.022

Cited by 55 publications

(19 citation statements)

References 3 publications

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“…(1) there exists a ∈ ]0, 1[ such that d(f (x), f (y)) a · d(x, y), for each x, y ∈ X with x y; (2) there exists x 0 ∈ X such that x 0 f (x 0 ); (3) if an increasing sequence (x n ) converges to x in X, then x n x for all n ∈ N.…”

Section: Theorem 12 (See Nieto and Rodríguez-lópezmentioning

confidence: 99%

Fixed point theorems for generalized contractions in ordered metric spaces

O’Regan

Petruşel

2008

Journal of Mathematical Analysis and Applications

295

146

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The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petruşel, I.A. Rus [A. Petruşel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.

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Section: Theorem 12 (See Nieto and Rodríguez-lópezmentioning

confidence: 99%

Fixed point theorems for generalized contractions in ordered metric spaces

O’Regan

Petruşel

2008

Journal of Mathematical Analysis and Applications

295

146

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“…Popa [12,13] initiated the study of fixed point for mappings satisfying implicit relations satisfying ϕ-map. After that Berinde [5] proved some constructive fixed point theorems for almost contractions for an implicit relation, which generalize related results (see [2,3,6,7,15]). …”

Section: Introductionmentioning

confidence: 60%

Fixed point theorems for set valued mappings in partially ordered $G$-metric space

Kumar

2014

Tbilisi Math. J.

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“…Later, so many results were proved on existence and uniquenss of fixed point in partially ordred metric spaces, see e.g. [2,3,4,8,9,10,11,14,16,18,19,22].…”

Section: Introductionmentioning

confidence: 99%